Question

A rectangular deck has a length of 12 feet and a perimeter of 36 feet

Answer 1

We are given the following information

Length of rectangular deck = 12 feet

Perimeter of rectangular deck = 36 feet

Recall that the perimeter of rectangular shape is given by

`P=2l+2w_{}`

Where l is the length, w is the width, and P is the perimeter of the rectangle.

Let us substitute the given values and solve for width (w)

`\begin{gathered} P=2l+2w_{} \\ 36=2(12)+2w_{} \\ 36=24+2w_{} \\ 36-24=2w_{} \\ 12=2w_{} \\ (12)/(2)=w \\ 6=w \\ w=6\: feet \end{gathered}`

Therefore, the deck's width is 6 feet

Recall that the area of a rectangular shape is given by

`A=l\cdot w`

Where l is the length and w is the width of the rectangle.

`\begin{gathered} A=l\cdot w \\ A=12\cdot6 \\ A=72\: ft^2 \end{gathered}`

Therefore, the deck's area is 72 square feet.