Question

The perimeter of a rectangle is 54 inches, and its area is 180 in^2. Find its length and width.

Answer 1

so for perimeter

P = 2l + 2w

or

54 = 2l + 2w (equation 1)

next for the area

A= lw

or

180 = lw (equation 2)

rewrite equation 2 and

27 - w = l

and substitute into equation 2

180 =(27 - w)w

so you now have a quadratic that needs to be solved

\[-(w^2 - 27w + 180) = 0\]

solve for the w, but only use the positive answers,

then substitute into equation 1 to find l.