Question

The perimeter of a rectangle is 84. The length is 10 more than three times the width. Find the length and width.

Answer 1

The length is 34 and the width is 8

Explanation:

Let w represent the width and let the length be represented by (3w + 10)

Use the perimeter formula, P = 2l + 2w

Plug in the perimeter, w, and the expression for the length:

P = 2l + 2w

84 = 2(3w + 10) + 2w

Solve for w:

84 = 2(3w + 10) + 2w

84 = 6w + 20 + 2w

84 = 8w + 20

64 = 8w

8 = w

Plug in 8 as w into the expression for the length to find the length:

3w + 10

3(8) + 10

24 + 10

= 34

So, the length is 34 and the width is 8