Question

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

Answer 1

Solution:

Let l be the length
Let b be the breadth

(l - 10%) = l - (10/100)l = (90/100)l = (9/10)l

(b + 20%) = b + (20/100) = (120/100)b = (12/10)b

P = 2(l + b)

240 = 2(l + b)

120 = (l + b) ... Eq. 1

New decrease and increase:

240 = 2[(9/10)l + (12/10b)]

100[120 = 9/10l + 12/10b]100

1200 = 9l + 12b

Simplify by dividing by 3

(1200 = 9l + 12b)

400 = 3l + 4b ... Eq. 2

Use Eq. 1 and Eq. 2 to eliminate

Eq. 1

120 = l + b ... multiple 3

360 = 3l + 3b

Then subtract to Eq. 2

400 = 3l + 4b
360 = 3l + 3b

b = 40

Use Eq.1 to find l

120 = l + b

120 = l + 40

l = 120 - 40 = 80.

Therefore, length is 80cm and breadth is 40 cm.

Hope it will help.