The perimeter of a rectangle is 38 inches, and its area is 90 in2. Find its length and width.

Question

The perimeter of a rectangle is 38 inches, and its area is 90 in². Find its length and width.

longer side	in
shorter side	in

Answer 1

I duplicated Brenda's result before opening this page. The only difference is the way I generated the quadratic. I started from half of the perimeter as she did.

W + L= 19

Then I multiplied both sides by W to get

W² + LW = 19W

Substituted LW = 90

W² + 90 = 19W

and subtracted 19W to form the same quadratic she had.

The rest is the same as her answer L = 10, W = 9.

Answer 2

Longer side is 10 inches

Shorter side is 9 inches

Given

Perimeter 38 in

Area = 90 in

And

Perimeter = 2(length) + 2(width)

Let P = Perimeter

Let L = length and the longer side

Let W = width the shorter side

Area = length times width

P = 2L + 2W = 38

Divide the equation by 2

L + W = 19

Therefore

L = 19 - W

The area can be written in terms of W

90 = W(19 - W)

90 = 19W - W²

We can make a quadratic by bringing the variables over to one side

90 - 19W + W² = 0

Rearranging

W² - 19W + 90 = 0

Factoring

(W - 10)(W - 9) = 0

Since L is the longer side, W can only equal 9 inches

L = 19 - 9 = 10 inches

I hope this helps