Question

determine the width of a concrete walkway surrounding the adult pool. use the fax below to calculate the width. You will submit a sketch of your work along with the mathematics to support your answer.

Answer 1

Given the sketch of the pool:

The total area of the Adult pool is:

$A=15000\text{ ft}^2$

According to the sketch, this is equivalent to:

$(120+2x)(70+2x)=15000$

Solving for x (the width of the walkway):

$\begin{gathered} 120\cdot70+120\cdot2x+70\cdot2x+4x^2=15000 \\ 8400+380x+4x^2=15000 \\ 4x^2+380x-6600=0 \\ \\ \Rightarrow x^2+95x-1650=0 \end{gathered}$

This is equivalent to:

$\begin{gathered} x^2+95x-1650=(x+110)(x-15)=0 \\ \\ \Rightarrow x+110=0\Rightarrow x=-110\text{ \lparen Incorrect, the width must be positive\rparen} \\ \Rightarrow x-15=0\Rightarrow x=15\text{ ft \lparen Correct answer\rparen} \end{gathered}$