The width of a rectangle is 3/4 the length. The perimeter of the rectangle becomes 50 cm when the length and width are each increased by 2 cm. Find the length and width.

Answer 1

2(L+2) + 2(w+2) = 50

2L + 4 + 2w + 4 = 50

2L + 2w + 8 = 50

2L + 2w = 42

L +w = 21

(3/4)w + w = 21

(3/4)w + (4/4)w = 21

(7/4)w = 21

w = 21 * 4/7 = 12

L = 9

The original rectangle is 12 by 9.

the larger rectangle is 14 by 11 which has area 2(14)+2(11) = 28 + 22 = 50