Please solve

Question

A rectangle is 11 cm narrower than is long. The length is two sevenths of the perimeter. Find the length and the width.

Answer 1

Karen,

 

Let width = W and length = L

If the width is 11 cm narrower than the length, then

 

W = L - 11

 

The perimeter is 2L + 2W.

If the length is 2/7 or the perimeter, then

 

L = (2/7)[2L + 2W]

 

Substitute W = L -11

 

L = (2/7)[2L + 2(L - 11)] = (2/7)[2L + 2L -22] = (2/7)(4L -22)

 

Multiply both sides by 7 and simplify the right hand side:

 

7L = 8L - 44

 

L = 44 cm

 

W = (44 - 11) cm = 33 cm

 

Check answer:  Perimeter P = 2L + 2W = 154 cm

 

44/154 = 22/77 = 2/7