The perimeter of a rectangle is 7 times its width. What are its sides if the area is 40?

If p is the perimeter, A the area, l and w  the sides of a
rectangle , then,

 P =
2(l+w).

A = lw.

Given that p =
7w and A = 40.

Therefore , the perimmeter equation could be
written  as:

7w = 2(l+w)...(1) and area equation as:  40 =
lw...(2).

From (1) , we get 7w = 2l+2w. Or 2l = 7-2w = 5w.
So l = 5w/2.

We put l = 5w/2 in eq
(2):

40 =  (5w/2)w =
5w^2/2.

Multiply both sides by
2.

80 = 5w^2.

Divide both
sides by 5:

16 = w^2.

Take
square root:

4 = w.

Therefore
from (2) 40 lw, Or 40 =l*4. So we get l= 40/4 =
10.

Therefore the length and width of the given rectangle
are 10 and 4 .