Question

A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 360 square yards find the length in the width. Use the formula, area= length× width.The parking lot has a width of ___ yards.

Answer 1

The area of a rectangle is given by the following expression:

`\text{area}=\text{length}\cdot\text{width}`

We know that the length of the parking lot is 9 yards greater than the width, this means that if we add 9 yards to the width we will have the length.

`\text{length}=\text{width}+9`

By applying the second expression on the first one and making it equal to the area of the parking lot we can determine the width.

`\begin{gathered} 360=(\text{width}+9)\cdot\text{width} \\ 360=width^2+9\cdot width \\ \text{width }^2+9\text{width}-360=0 \end{gathered}`

We need to solve the second degree equation to determine the width.

`\begin{gathered} \text{width}=\frac{-9\pm\sqrt[]{9^2-4\cdot1\cdot(-360)}}{2\cdot1} \\ \text{width}=\frac{-9\pm\sqrt[]{81+1440}}{2}=(-9\pm39)/(2) \\ \text{width}=(-9+39)/(2)=(30)/(2)=15 \end{gathered}`

The width of the parking lot is 15 yards.

The length is the width added by 9 yards, which is equal to 24 yards.