Question

A rectangle has sides of 4x cm and x cm. the sides of the rectangle are all increased by the same length.if the perimeter of the larger rectangle is 10x + 16, what is the length added to each side, in centimeters?

Answer 1

4 cm

Explanation:

The perimeter of the original rectangle is ...

P = 2(L+W) = 2(4x + x) = 10x

The perimeter of the larger rectangle after we add "a" to each side is ...

P = 2(L +W)

= 2((4x+a) +(x+a))

= 10x +4a = 10x +16

4a = 16 . . . . . subtract 10x from both sides

a = 4 . . . . . . . divide by 4

The length added to each side is 4 cm.