ANSWER
Length = 12 ft;
Width = 6 ft
Step-by-step explanation
We have that the ratio of the length and width is 6 : 3.
The area of the rectangle is 72 square feet.
The area of a rectangle is given as:
A = L * W
where L = length
W = width
From the ratio, we have that:
L : W = 6 : 3
That is:

Therefore, the area of the rectangle is:
![\begin{gathered} 72\text{ = L }\cdot\text{ W} \\ 72\text{ = 2W }\cdot\text{ W} \\ 72=2W^2 \\ Divide\text{ through by 2:} \\ W^2\text{ = }(72)/(2)=\text{ 36} \\ Find\text{ the square root of both sides:} \\ W\text{ = }\sqrt[]{36} \\ W\text{ = 6 ft} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/olm3eqnb41elsvnl886dbw3zpu3s100hzj.png)
Therefore, the length is:
L = 2 * W
L = 2 * 6
L = 12 ft
Therefore, the dimensions of the rectangle is length of 12 ft and width of 6 ft.