Chapter 7.2, Problem 7P

To determine

To find: The width of the walkway.

Answer to Problem 7P

The width of the walkway is 3.36 m.

Explanation of Solution

Given:

The length of the swimming pool 10 m.

The width of the swimming pool 8 m.

Calculation:

Consider the constant width of the walkway is x .

The total area of the swimming pool and the walkway is

  $\begin{array}{l}\left(l+x\right)\left(b+x\right)=8\times 10+72\\ \left(10+x\right)\left(8+x\right)=152\\ x^2+18x+80=152\\ x^2+18x-72=0\end{array}$

The solution of the given equation is obtained by using the quadratic formula.

For a quadratic equation in the form of $a{x}^2+bx+c=0$ , the solution of this equation is given by

  $x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Comparing the given equation with the standard quadratic equation, the coefficients are:

  $\begin{array}{l}a=1\\ b=18\\ c=-72\end{array}$

Substituting these in the formula for the roots.

First take the positive sign.

  $\begin{array}{c}{x}_1=\frac{-\left(18\right)\pm \sqrt{{\left(18\right)}^2-4\times 1\times \left(-72\right)}}{2\times 1}\\ =\frac{-18\pm \sqrt{324+288}}{2}\\ =\frac{-18\pm 24.73}{2}\\ =3.36,-21.36\end{array}$

The width cannot be negative.

The width of the walkway is 3.36 m.

Therefore, the width of the walkway is 3.36 m.