The area of a rectangular sticker is 54 square centimeters. The perimeter is 30 centimeters. What are the dimensions of the sticker?

Answer 1

Area is length times width, so L x W = 54

Perimeter is twice the length plus twice the width, so 2L + 2W = 30.

You cannot solve an equation with two variables (letters), so you need to use one equation to substitute into the other. Let's solve the second equation for L.

2L + 2W = 30

Divide everything by 2: L + W = 15

Subtract W from both sides: L = 15 - W

Now we plug into the other equation. Instead of using L, we'll use 15 - W

(15-W) x W = 54

Distribute the W: W^2 - 15W = 54

Move the 54 over by subtracting from both sides: W^2 - 15W - 54 = 0

Now use FOIL backwards to determine what W could be: (W - 18 )(W + 3)

First: W x W = X^2

Outside: W x 3 = 3W

Inside: -18 x W = -18W

Last: -18 x 3 = -54

Combine 3W and - 18W and you get -15W.

So, W = 18 or W = -3. But your width cannot be negative, so W = 18 is your answer.

When you know the width, you can find the length, because W x L = 54

18 X L = 54

Divide both sides by 18: L = 3

Width is 18 and Length is 3.