Question

If the length of a pool is 8 more than twice the width and the total area is 960 square feet, find the length and width of the rectangular landscape element.

Answer 1

l=48, w=20

Explanation:

Let the width of the pool be w feet, then the length will be:

`l = 2w + 8`

The area of the pool is 960 square feet.

This means that:

`w(2w + 8) = 960`

Expand and rewrite in standard form to get:

`2 {w}^(2) + 8w - 960 = 0`

`{w}^(2) + 4w - 480 = 0`

`{w}^(2) + 24w - 20w- 480 = 0`

`{w}(w+ 24) - 20(w + 24) = 0`

Factor to get:

`(w+ 24)(w - 20) = 0`

`w = - 24 \: or \: w = 20`

We discard the negative value because magnitude is positive.

This means

`l = 2 * 20 + 8 = 48`