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Chapter 10: Q 96 (page 1181)

Yvette wants to put a square swimming pool in the corner of her backyard. She will have a 3footdeck on the south side of the pool and a 9footdeck on the west side of the pool. She has a total area of 1080squarefeetfor the pool and two decks. Solve the equation s+3s+9=1080for s, the length of a side of the pool.

Short Answer

Expert verified

The length of the side of the pool is,27foot.

Step by step solution

01

Step 1. Given Information.

The equation is,

s+3s+9=1080.

02

Step 2. The length of the side of the pool.

Given, s+3s+9=1080

Simplifying the equation,

鈬�s2+3s+9s+27=1080鈬�s2+12s+27-1080=0鈬�s2+12s-1053=0鈬�s2+12s=1053

Using the completing the square method.

We will be adding the square of the half of 12on both sides,

鈬�s2+12s+12122=1053+12122鈬�s2+12s+36=1053+36鈬�s2+12s+36=1089

Taking the left side as a binomial square.

鈬�s+62=1089

Taking the square root on both sides,

鈬�s+6=1089鈬�s+6=卤33

Solving for the value of s,

鈬�s=卤33-6鈬�s=33-6or,s=-33-6鈬�s=27,-39

The length of the side of the pool is27foot.

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