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

Answer:

l=48, w=20

Step-by-step 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

$l = 2 \times 20 + 8 = 48$