Question

Chloe discovers that her rectangular shed is 6 feet longer than three times the width. If the perimeter of the shed is 100 feet, find the dimensions. (Recall: the perimeter of a rectangle is given by the formula P = 2 L + 2 W .)

Answer 1

11 feet by 39 feet.

Explanation:

In this case, the perimeter, P, is 100 ft.

If the length of the shed is 6 feet longer than three times the width, that means that the length, L, is equivalent to 6 plus 3 times the width, W.

So, we have an equation: P = 2 * L + 2 * W.

100 = 2 * (6 + 3W) + 2 * W

100 = 12 + 6W + 2W

100 = 12 + 8W

8W + 12 = 100

8W = 88

W = 11

And so, we know that the width is 11 feet.

To solve for the length...

L = 6 + 3W

L = 6 + 3 * 11

L = 6 + 33

L = 39

So, the length is 39 feet.

Now, you have the dimensions of the shed: 11 feet by 39 feet.

Hope this helps!