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The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Solution:

Given, the perimeter of a rectangle is 240 cm.

The perimeter is the same when the length is increased by 10% and its breadth is decreased by 20%.

We have to find the length and breadth of the rectangle.

We know, perimeter of rectangle = 2(length + breadth)

According to the question,

2(length + breadth) = 240

Length + breadth = 240/2

Length + breadth = 120

Length = 120 - breadth ------------------ (1)

New length = length + 10% length

= 110/100 length

New breadth = breadth - 20% breadth

= 80/100 breadth

Since, the perimeter is the same.

2(110/100 length + 80/100 breadth) = 240

1.1 length + 0.8 breadth = 120 --------------- (2)

On solving (1) and (2),

1.1(120 - breadth) + 0.8 breadth = 120

132 - 1.1 breadth + 0.8 breadth = 120

breadth(0.8 - 1.1) = 120 -132

0.3 breadth = 12

Breadth = 12/0.3

Breadth = 40 cm

From (1), length = 120 - 40

Length = 80 cm

Therefore, the length and breadth of the rectangle is 80 cm and 40 cm.

✦ Try This: The perimeter of a rectangle is 300 cm. If its length is increased by 30% and its breadth is decreased by 10%, we get the same perimeter. Find the length and breadth of the rectangle.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 2

NCERT Exemplar Class 8 Maths Chapter 4 Problem 96

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Summary:

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. The length and breadth of the rectangle is 80 cm and 40 cm

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