Question

The length of a rectangle is three times its width.If the area of the rectangle is 147 yd?, find its perimeter.

Answer 1

Let's call L the length of the rectangle and W the width of the rectangle

We know the length is 3 times its width:

L = 3W

The area of a rectangle is:

A=L*W

Substituting the condition above, we have:

A = (3W)*W

Operating:

`A=3W^2`

We know the area is 147 yd^2, so we equate:

`3W^2=147`

Solve for W:

`W^2=(147)/(3)=49`

Taking the square root on both sides:

`W=\sqrt[]{49}=7`

The width is 7 yd. Now we can easily find the length:

L=3W=3*7=21 yd

Finally, we calculate the perimeter of the rectangle. Recall the perimeter is calculated with the formula:

P=2L+2W

Thus, using the known values:

P=2*21+2*7=42 + 14 = 56 yd

The perimeter of the rectangle is 56 yd