Question

Please Help Me Out!!
The length of a rectangle is twice its width. If the area of the rectangle is 128 yd^2, find its perimeter.

Answer 1

Knowns:

Area = length * width
Perimeter = 2*length + 2*width
Length = 2* width
Area = 128 yd^2

Unknowns:

Perimeter.

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Perimeter = 2*l + 2*w

Since length = 2*width

Perimeter = 4*w + 2*w = 6*w


Now,

Area = length * width = 2*width * width = 2*width^2

Rearrange to solve for width:

A = 2*w^2
A/2 = w^2
sqrt(A/2) = w

We know Area (A) is 128, so after subbing in that value we get:

w = sqrt(128/2) = 8

Now insert the formula for width into our refined formula for perimeter

P = 6*w

P = 6*8 = 48 yd

Therefore, the perimeter is 48 yds.