Question

the area of a garden is 81 square yards. The length is nine times the width. find the width of the garden.

Answer 1

The area of a rectangular or square shape can be found by using the following formula:

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

We were told that the length is nine times the width, therefore:

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

If we replace the expression for the length above on the expression for the area, we will obtain the following formula:

`A=9\cdot\text{width}^2`

We can replace A with the value of the area to solve for the width:

`\begin{gathered} 81=9\cdot\text{width}^2 \\ \text{width}^2=(81)/(9) \\ \text{width}^2=9 \\ \text{width}=\sqrt[]{9} \\ \text{width}=3\text{ yards} \end{gathered}`

The width of the garden is 3 yards.