Question

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

Answer 1

Let the length and breadth of the first rectangle be L and B respectively.

So, 2(L+B) = 240
or L + B = 240/2
or L = 120 - B -----(1)

Now, length of second rectangle = L - 10/100 L = L - L/10 = 9L/10
and breadth of second rectangle = B + 20/100 B = B + B/5 = 6B/5

So, 2(9L/10 + 6B/5) = 240
or (9L + 12B)/10 = 120
or 3(3L + 4B) = 1200
or 3L + 4B = 400
or 3(120 - B) + 4B = 400
or 360 - 3B + 4B + 400
or B = 400 - 360 = 40 cm

So, L = 120 - 40 = 80 cm

So, length of 1^st rectangle = 80 cm
and breadth of 1^st rectangle = 40 cm

Also, length of 2^nd rectangle = 9*80/10 = 72 cm
and breadth of 2^nd rectangle = 6*40/5 = 48 cm