Chapter 8.3, Problem 35PPS

a.

To determine

To write: An expression that represents the area of the court.

Answer to Problem 35PPS

  $18y^2+9y-20\text{sq}\text{. feet}$

Explanation of Solution

Given:

The width of the sand volleyball court is $6y-5$ feet and that of length is $3y+4$ feet

Calculation:

The area of the sand volleyball court is the product of length and width.

Hence, area of the sand volleyball court is given by

  $\begin{array}{l}\left(6y-5\right)\left(3y+4\right)\\ =18y^2+24y-15y-20\\ =18y^2+9y-20\text{sq}\text{. feet}\end{array}$

b.

To determine

To write: Find the area of the court.

Answer to Problem 35PPS

  $1519\text{ sq}\text{. feet}$

Explanation of Solution

Given:

The length of the sand volleyball court is $31$ feet

Calculation:

It has been given that the length of the sand volleyball is represented by $3y+4$ . So, this expression should be equal to 31

  $\begin{array}{c}3y+4=31\\ 3y=27\\ y=9\end{array}$

From part (a), the area of the rectangle is represented by $18y^2+9y-20$

So, substituting $y=9$ in this expression to find the area of the rectangle

  $\begin{array}{l}18{\left(9\right)}^2+9\left(9\right)-20\\ =1458+81-20\\ =1519\text{ sq}\text{. feet}\end{array}$