Math Help!!!

A rectangular table is six times as long as it is wide. If the area is 54ft^2, find the width of the table.

width = w

length = l

Area = A

$\begin{array}{rcll} l &=& 6w \\ A &=& 6w \cdot w \\ A &=& 6w^2 \qquad & | \qquad : 6\\ \frac{A}{6} &=& w^2 \qquad & | \qquad \sqrt{}\\ \sqrt{\frac{A}{6}} &=& w \\ w &=& \sqrt{\frac{A}{6}} \qquad & | \qquad A = 54\ \text{ft.}^2\\ w &=& \sqrt{\frac{54\ \text{ft.}^2}{6}} \\ w &=& \sqrt{\frac{9\cdot 6 \ \text{ft.}^2}{6}} \qquad 54 = 9\cdot 6\\ w &=& \sqrt{9 \ \text{ft.}^2} \\ w &=& 3 \ \text{ft.} \\\\ l &=& 6w \\ l &=& 6\cdot 3 \ \text{ft.} \\ l &=& 18 \ \text{ft.} \\ \end{array}\\$

The width of the table is 3 ft.

The length of the table is 18 ft.

A rectangular table is six times as long as it is wide. If the area is 54ft^2, find the width of the table.

Let the width=W, the length is=6W, but

Area=W X 6W

54=6W^2 divide both sides by 6

9=W^2 take the sqrt of both sides

W=3 feet width of table

3 X 6=18 feet length of the table.