The length of a rectangle is five times it’s width if the area of the rectangle is 180 yd.² find the perimeter

Answer 1

Good Morning, Valerie,

Let's solve the problem as follows, okay?

A = L x W A equals area, L equals length, and W equals width. We good so far?

Let the following expressions represent the length and width:

L = 5x <-----the length of a rectangle is five times its width.

W = x <-----We arbitrarily assign x as the width because it is not given.

Therefore:

A = L x W

180 = 5x * x

180 = 5x ^ 2

36 = x ^2

sq rt 36 = x

6 = x

Width of the rectangle is 6

Then to determine the length we need to substitute 6 for x in our original expression, right?

L = 5 (x)

L = 5 (6)

L = 30

Length of the rectangle is 30.

Now, let's check our work, shall we?

First, let's use the formula for determining the area of the rectangle by substituting our values, right?

A = L x W

180 = 30 * 6

180 = 180

The above values satisfy the solution and check out, however, your problem is asking for the perimeter, right?

The formula for the perimeter of a rectangle is as follows:

P = 2 (L + W) or P = 2 (L) + 2 (W) It matters little which formula you choose, but I prefer the first. Therefore:

P = 2 (6 + 30)

P = 2 (36)

P = 72

The perimeter of this rectangle is 72.

I hope this solution assists you and that you have a great day today. If you have any further questions or feedback, please just leave a comment under this discussion thread. If you need further assistance, please feel free to reach out to any of our qualified tutors. Best.

Answer 2

Hello Valerie

L = 5W

A = L x W = 180 yd^2

5W x W = 180

5W^2 = 180

W^2 = 180 / 5 = 36

W = square root of 36 = 6 yd

L = 5W = 5 x 6 = 30 yd

Perimeter, P = 2(L + W)

= 2(30 + 6)

= 2(36) = 72 yd