The length of a rectangle is twice its width. The perimeter is 60 ft. Find its area.

Question

Which of the following equations could be used to solve the problem?

2x + 2(x - 3) = 54

2x + 2x - 3 = 54

2x - 3 = 54

Answer 1

Hello, Ashley,

We have two unknowns, so we need to find at least two equations.

Let's set the following definitions:

A = Area of the rectangle

W = Width " "

L = Length " "

P = Perimeter " "

We know that A=W*L

We are told that L=2W

A Perimeter is the sum of all the sides: P=2L+2W

And we know that P=60ft

Since we know that L=2W, use that in the Perimeter equation:

P=2(2W)+2W

P=6W

We know P=60ft, so 60ft=6W

Therefore, W=10ft

To find L, use L=2W: L=2*(10) or 20ft

The area is W*L or (20ft)*(10ft) = 200ft²

But we don't seem to be done, yet. The question asks which of the formulas can be used. I'm not clear what "x" represents, and, in any event, when I solve them for x, I get numbers that don't relate to the problem.

My answers for x:

2x + 2(x - 3) = 54 x=15

2x + 2x - 3 = 54 x = 57/4 (ugly)

2x - 3 = 54 x = 57/2

I don't see how these apply to the problem, sorry.

Bob