Question

The length of a rectangle is the same as its width. If the perimeter is 32 M what is its area?

Answer 1

The perimeter of a rectangle is calculated using the formula:

`P=2(l+w)`

The question gives that the length and width of the rectangle are equal. This means that:

`l=w`

Therefore, the perimeter will be calculated to be:

`\begin{gathered} P=2(l+l)=2(2l) \\ P=4l \end{gathered}`

The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:

`\begin{gathered} 32=4l \\ l=(32)/(4) \\ l=8 \end{gathered}`

Using the formula for the area:

`A=l^2`

Therefore, the area will be:

`\begin{gathered} A=8^2 \\ A=64\text{ m}^2 \end{gathered}`

The area is 64 square meters.