Chapter 14, Problem 45SGR

To determine

To calculate: The length of the tennis court.

Answer to Problem 45SGR

Therequired length of the tennis court is $8x+6\text{feet}$ .

Explanation of Solution

Given Information:

The expression for the area of the tennis court is $24x^2+18x$ .

Width of the tennis court is $3x\text{feet}$ .

Formula Used:

Area of a rectangle is:

  $\text{Area}=\text{Length}\times \text{Width}$

Calculation:

The given expressionof the area of the tennis court is $24x^2+18x$ .

Find the length of the tennis court. Use the formula $\text{Area}=\text{Length}\times \text{Width}$

  $\begin{array}{c}\text{Area}=\text{Length}\times \text{Width}\\ \text{Length}=\frac{\text{Area}}{\text{Width}}\\ =\frac{24x^2+18x}{3x}\end{array}$

Find the division for the expression $\frac{24x^2+18x}{3x}$ .

Take the common term $3x$ out from the numerator and simplify.

  $\begin{array}{c}\frac{24x^2+18x}{3x}=\frac{3x\left(8x+6\right)}{3x}\\ =8x+6\end{array}$

Hence, the required length of the tennis courtis $8x+6\text{feet}$ .