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.

Perimeter of the given rectangle = 240 cm

Let the length of the rectangle = x cm

Let the breadth of the rectangle = y cm

According to the question

2(x + y) = 240

x + y = 240⋯(i)

(divide by 2 on both the sides)

Let the new length be

Let the new breath be

According to the question

(divide by 2 on both the sides)

From

(take L.C.M on both side and solve)

x = 2y

(multiply by 10 on both the sides and solve)

x-2y = 0⋯(iii)

subtracting (iii)from (i)

x-2y-x-y = -120

-3y = -120

y = 40

Put the value of y in (i)

x + y = 120

x = 120-40

x = 80

The breath = 40 cm

The length = 80 cm

Hence, length of the 2^nd rectangle

Breath of the 2^nd rectangle