Question

3.) The ratio of the measures of the length and width of a rectangle is 6:3. The areaof the rectangle is 72 square feet. Find the dimensions of the rectangle,

Answer 1

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:

`\begin{gathered} (L)/(W)\text{ = }(6)/(3) \\ Cross\text{ multiply:} \\ 3L\text{ = 6W} \\ \text{Divide through by 3:} \\ L\text{ = 2W} \end{gathered}`

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}`

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.