Explore Exams
Login Signup
Sign in Open App

All questions of Area & Perimeter for RRB Group D / RPF Constable Exam

Clear all your doubts with EduRev

If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.
  • a)
    6%
  • b)
    4%
  • c)
    5%
  • d)
    9%
Correct answer is option 'C'. Can you explain this answer?

Malavika Rane answered
Understanding the Problem
To find the percentage increase in the diagonals of a rectangle when its sides are increased by 5%, we start by recalling the formula for the diagonal of a rectangle. The diagonal (d) can be calculated using the Pythagorean theorem:
d = √(length² + width²)
Initial Dimensions
- Let the initial length of the rectangle be L.
- Let the initial width of the rectangle be W.
Increased Dimensions
- After a 5% increase:
- New length, L' = L + 0.05L = 1.05L
- New width, W' = W + 0.05W = 1.05W
Calculating the Initial Diagonal
- Initial diagonal, d = √(L² + W²)
Calculating the New Diagonal
- New diagonal, d' = √((1.05L)² + (1.05W)²)
- Simplifying this, we get:
- d' = √(1.1025L² + 1.1025W²)
- d' = √(1.1025(L² + W²)) = 1.05√(L² + W²)
- Thus, d' = 1.05d
Percentage Increase in Diagonal
- The increase in diagonal = d' - d = 1.05d - d = 0.05d
- Percentage increase = (Increase / Original) × 100
- Percentage increase = (0.05d / d) × 100 = 5%
Conclusion
The percentage increase in the diagonals of the rectangle is 5%. Thus, the correct answer is option C.

If the ratio of the area of two square is 9 : 1 the ratio of their perimeters is ?
  • a)
    9:1
  • b)
    3:1
  • c)
    3:4
  • d)
    1:3
Correct answer is option 'B'. Can you explain this answer?

Gowri Dasgupta answered
Understanding the Ratio of Areas
When we say that the ratio of the areas of two squares is 9:1, we can denote the side lengths of the squares as S1 and S2. The area of a square is calculated as the side length squared.
- Area of Square 1 = S1²
- Area of Square 2 = S2²
Given the ratio:
- S1² : S2² = 9 : 1
This indicates that S1² = 9 * S2².
Finding the Ratio of Side Lengths
To find the side lengths:
- S1/S2 = √(S1²/S2²) = √(9/1) = 3/1
This shows that the side length of Square 1 is 3 times that of Square 2.
Calculating the Perimeters
Now, we can calculate the perimeters of both squares. The perimeter (P) of a square is given by:
- P = 4 * Side Length
Thus, we have:
- Perimeter of Square 1 = 4 * S1
- Perimeter of Square 2 = 4 * S2
Using the ratio of side lengths:
- P1/P2 = (4 * S1) / (4 * S2) = S1/S2 = 3/1
Conclusion
Therefore, the ratio of the perimeters of the two squares is 3:1.
The correct answer is option 'B'.

One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?
  • a)
    12.56 cm2
  • b)
    14.56 cm2
  • c)
    16.76 cm2
  • d)
    22.56 cm2
Correct answer is option 'C'. Can you explain this answer?

Nilesh Banerjee answered
Given data:
One side of parallelogram = 8.06 cm
Perpendicular distance from opposite side = 2.08 cm

Calculating the area of the parallelogram:
To find the area of a parallelogram, we use the formula: Area = base x height

Base:
The given side of the parallelogram is considered as the base.
Base = 8.06 cm

Height:
The perpendicular distance from the opposite side is considered as the height.
Height = 2.08 cm

Area calculation:
Area = base x height
Area = 8.06 cm x 2.08 cm
Area ≈ 16.76 cm²
Therefore, the approximate area of the parallelogram is 16.76 cm². Hence, the correct answer is option 'C'.

A hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m. the cost of flooring the verandah at the rate of 3.50 per sq. meter is ?
  • a)
    Rs. 500
  • b)
    Rs. 600
  • c)
    Rs. 700
  • d)
    Rs. 800
Correct answer is option 'C'. Can you explain this answer?

Gowri Dasgupta answered
Understanding the Dimensions
To find the cost of flooring the verandah, we first need to calculate the area of the verandah. The hall measures 20 m in length and 15 m in breadth. The verandah surrounds this hall uniformly with a width of 2.5 m.
Calculating Total Dimensions
- Length of the hall = 20 m
- Breadth of the hall = 15 m
- Width of the verandah = 2.5 m
Now, we need to calculate the overall dimensions including the verandah:
- Overall length = 20 m + 2.5 m + 2.5 m = 25 m
- Overall breadth = 15 m + 2.5 m + 2.5 m = 20 m
Calculating Areas
- Area of the hall = Length × Breadth = 20 m × 15 m = 300 sq. m
- Area of the hall including the verandah = Overall Length × Overall Breadth = 25 m × 20 m = 500 sq. m
Determining the Area of the Verandah
To find the area of the verandah, we subtract the area of the hall from the total area:
- Area of the verandah = Total Area - Area of the Hall = 500 sq. m - 300 sq. m = 200 sq. m
Calculating the Cost
Next, we calculate the cost of flooring the verandah at the rate of Rs. 3.50 per sq. meter:
- Cost = Area of the Verandah × Rate per sq. meter = 200 sq. m × Rs. 3.50 = Rs. 700
Final Answer
Thus, the cost of flooring the verandah is Rs. 700, which corresponds to option 'C'.

The area of a rectangle, 144 m long is the same as that of a square having a side 84 m long. The width of the rectangle is ?
  • a)
    7 m
  • b)
    14 m
  • c)
    49 m
  • d)
    Cannot be determined
Correct answer is option 'C'. Can you explain this answer?

Gowri Dasgupta answered
Understanding the Problem
To find the width of the rectangle, we first need to understand the areas involved. We have a rectangle with a length of 144 m and a square with a side length of 84 m. The problem states that their areas are equal.
Calculating the Area of the Square
- The area of the square can be calculated as:
- Area = side × side
- Area = 84 m × 84 m = 7056 m²
Calculating the Area of the Rectangle
- The area of the rectangle is given by:
- Area = length × width
- Area = 144 m × width
Setting the Areas Equal
Since the areas are equal, we can set up the equation:
- 144 m × width = 7056 m²
Solving for Width
Now, let’s solve for the width:
- width = 7056 m² / 144 m
- width = 49 m
Conclusion
Thus, the width of the rectangle is 49 m. Therefore, the correct answer is option 'C'.
This problem illustrates how to equate areas of different shapes and solve for unknown dimensions, a common type of question in bank exams.

A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?
  • a)
    100 meters
  • b)
    66.66 meters
  • c)
    33 meters
  • d)
    (100/ √ 3 ) meters
Correct answer is option 'A'. Can you explain this answer?

Sonal Singh answered
Understanding the Problem
The problem states that a rectangular plot is half as long again as it is broad. This means if the width (b) of the plot is denoted as x, then the length (l) can be expressed as:
- Length: l = x + (1/2)x = (3/2)x
The area of the plot is given as 2/3 hectares.
Conversion of Area
To work with more familiar units, we convert hectares to square meters:
- 1 hectare = 10,000 square meters
- Therefore, 2/3 hectares = (2/3) * 10,000 = 6,666.67 square meters
Calculating Area
Now, the area (A) of the rectangle can be calculated using the formula:
- A = length * width
- A = (3/2)x * x = (3/2)x^2
Setting the area equal to the calculated area:
- (3/2)x^2 = 6,666.67
Solving for x
To find x, rearrange the equation:
- x^2 = (6,666.67 * 2) / 3
- x^2 = 4,444.44
- x = sqrt(4,444.44) ≈ 66.67 meters (width)
Now, we find the length:
- l = (3/2) * 66.67 ≈ 100 meters
Conclusion
Thus, the length of the plot is approximately 100 meters, confirming that option A is correct.

The cost of papering the four walls of a room is Rs. 48. Each one of length, breadth and height of another room is double that of this room.The cost of papering the walls of the new room is ?
  • a)
    Rs. 384
  • b)
    Rs. 298
  • c)
    Rs. 192
  • d)
    Rs. 96
Correct answer is option 'C'. Can you explain this answer?

Gowri Dasgupta answered
Understanding the Problem
To find the cost of papering the walls of a new room, we first need to analyze the relationship between the dimensions of the two rooms and their respective costs.
Dimensions of the Rooms
- Let the length, breadth, and height of the original room be L, B, and H respectively.
- The volume of the original room does not directly affect the wall papering cost, but the surface area does.
Calculating Surface Area of the Original Room
- The surface area of the four walls of a room can be calculated using the formula:
Surface Area = 2 * (L * H + B * H)
- For the original room, suppose the surface area is A square units. The cost of papering these walls is Rs. 48.
Dimensions of the New Room
- The new room has dimensions double that of the original:
- Length = 2L
- Breadth = 2B
- Height = 2H
Calculating Surface Area of the New Room
- The surface area of the new room:
New Surface Area = 2 * (2L * 2H + 2B * 2H) = 2 * 4 * (L * H + B * H) = 4 * A
Cost of Papering the New Room
- Since the surface area of the new room is four times that of the original room, the cost will also increase proportionally.
- Therefore, the cost of papering the new room = 4 * Rs. 48 = Rs. 192.
Conclusion
The cost of papering the walls of the new room is Rs. 192. Hence, the correct answer is option 'C'.

If the circumference of a circle is the 352 meters, then its area in m square is ?
  • a)
    9856
  • b)
    8956
  • c)
    6589
  • d)
    5986
Correct answer is option 'A'. Can you explain this answer?

Wizius Careers answered
circumference = 2πr = 2 x (22 / 7) x r = 352
⇒ r = (352 x 7) / (22 x 2) =56 cm
Now area = πr2 = (22 / 7) x 56 x 56 m2
= 9856 m2 

The ratio of the area of two square, one having and double its diagonal than the other is ?
  • a)
    2:1
  • b)
    3:1
  • c)
    3:2
  • d)
    4:1
Correct answer is option 'D'. Can you explain this answer?

Glance Learning Institute answered
Let the diagonal of one square be (2d) cm
Then, diagonal of another square = d cm
∴ Area of first square = [ 1/2 x (2d)2] cm2
Area of second square = (1/2 x d2) cm2
∴ Ratio of area = (2d)2/ d2
= 4/1 = 4: 1

The length of a rectangle room is 4 meters . if it can be partitioned into two equal square rooms . what is the length of each partition in meters ?
  • a)
    1
  • b)
    2
  • c)
    4
  • d)
    Data inadequate
Correct answer is option 'B'. Can you explain this answer?

Target Study Academy answered
Let the width of the room be x members
Then, its area = (4x) m2
Area of each new square room = (2x)m2
Let the side of each new room = y meters
Then, y2 = 2x
Clearly, 2x is a complete square when x=2
∴ y2 = 4
⇒ y = 2 m . 

If the circumference of a circle is the 352 meters, then its area in m square is ?
  • a)
    9856
  • b)
    8956
  • c)
    6589
  • d)
    5986
Correct answer is option 'A'. Can you explain this answer?

Wizius Careers answered
circumference = 2πr = 2 x (22 / 7) x r = 352
⇒ r = (352 x 7) / (22 x 2) =56 cm
Now area = πr2 = (22 / 7) x 56 x 56 m2
= 9856 m2 

The length of hall is (4/3) times its breadth. If the area of hall be 300 square meters, the difference between the length and the breadth is ?
  • a)
    15 meters
  • b)
    4 meters
  • c)
    3 meters
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Learnpro Institute answered
Let breadth = b meters.
Then, length = 4b/3 meters.
∵ b x 4b/3 = 300
⇒ b2 = 300 x 3/4
⇒ b2 = 225
∴ b = 15
Hence, required difference = [(Length) - (Breadth) ]
= 4b/3 - b
= b/3
= 15/3 m
= 5 m

The radius of a circle has been reduced from 9 cm to 7 cm . the appropriate percentage decrease in area is ?
  • a)
    31.5 %
  • b)
    39.5 %
  • c)
    34.5 %
  • d)
    65.5 %
Correct answer is option 'B'. Can you explain this answer?

Spectrum Coaching Institute answered
Original area = (22/7) x 9 x 9 cm2
New area = (22/7) x 7 x 7 cm2
∴ Decrease = 22/7 x [(9)2 -(7)2] cm2
=(22/7) x 16 x 2 cm2
Decrease percent = [(22/7 x 16 x 2) /( 7/22 x 9 x 9)] x 100 %
= 39.5 % 

The length of a rectangular plot is twice of its width. If the length of a diagonal is 9√5 meters, the perimeter of the rectangular is ?
  • a)
    27 m
  • b)
    54 m
  • c)
    81 m
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

T.S Academy answered
Let breadth = y meters,
Then, length = 2y meters
∴ Diagonal = √y2 + (2y)2
= √5y2 meters
So, √5y2 = 9 √5
∴ y= 9
Thus, breadth = 9 m and length = 18 m
∴ Perimeter = 2 (18 + 9) m = 54m.

The area of a circular field is 13.86 hectares . The cost of fencing it at the rate of 20 paisa per meter is ?
  • a)
    Rs. 277.20
  • b)
    Rs. 264
  • c)
    Rs. 324
  • d)
    Rs. 198
Correct answer is option 'B'. Can you explain this answer?

Wizius Careers answered
∵ 22/7 x r2 = 13.86 x 10000
⇒ r2 = (13.86 x 10000 x 7) / 22
∴ r = 210 m
⇒ Circumference = [2 x (22/7) x 210 ] m
= 1320 m
Cost of fencing = Rs. (1320 x 20)/100
= Rs . 264 

In a triangle ABC, BC = 5 cm AC = 12 cm and AB = 13 cm. The length of a altitude drawn from B on AC is ?
  • a)
    4 cm
  • b)
    5 cm
  • c)
    6 cm
  • d)
    7 cm
Correct answer is option 'B'. Can you explain this answer?

Aim It Academy answered
∵ s= (13 + 5 + 12) / 2 cm
= 15cm
s-a = 2 cm,
s-b = 10 cm and
s-c = 3 cm
⇒ Area = √ (15 x 2 x 10 x 3 ) cm2
= 30 cm2
⇒ (12 x h) / 2 = 30
∴ h = 5 cm

Chapter doubts & questions for Area & Perimeter - Mathematics for RRB Group D / RPF Constable 2025 is part of RRB Group D / RPF Constable exam preparation. The chapters have been prepared according to the RRB Group D / RPF Constable exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for RRB Group D / RPF Constable 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Area & Perimeter - Mathematics for RRB Group D / RPF Constable in English & Hindi are available as part of RRB Group D / RPF Constable exam. Download more important topics, notes, lectures and mock test series for RRB Group D / RPF Constable Exam by signing up for free.

Mathematics for RRB Group D / RPF Constable

174 videos|94 docs|92 tests

Top Courses RRB Group D / RPF Constable

© EduRev
Education Revolution
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily