Question

A rectangular bathroom mirror has an area of 32 square feet. Its perimeter is 24 feet. What

are the dimensions of the mirror?
feet by
feet

Answer 1

The dimensions are length = 8 and width = 4 feet.

Explanation:

Perimeter = 2(w + l) where w = width and l = length.

2(w + l) = 24

Area wl = 32

w = 32/l

Now substitute for w in the equation for the perimeter:

2(32/l + l) = 24

32/l + l = 12

Multiply through by l:

32 + l^2 = 12l

l^2 - 12l + 32 = 0

(l - 4)(l - 8) = 0

l = 4, 8

When l = 8, w = 32/8 = 4.

So l = 8, w = 4 ( length must be > width.