Question

The length of a rectangle is 6 in longer than its width. if the perimeter of the rectangle is 36 in , find its area.

Answer 1

`l = 6+w`

`P=36`

We know that perimeter is 2l + 2w, so we can calculate the perimeter.

`36=2l+2w`

Since we know that
`l=w+6`, we can plug it into the equation.

`36=2(w+6)+2w`

Simplify the equation by distributing.

`36=2w+12+2w`

Combine like terms.

`36=4w+12`

Subtract 12 from both sides.

`24=4w`

Divide both sides by 4.

`w=6in`

Now that we have the width, we can find the length.

`36=2l+12`

`24=2l`

`l=12in`

Now that we know the length and the width of the rectangle, we can determine the area.

`A=lw`

`A=(12in)(6in)`

`A=72in^2`

The area of the rectangle is 72in².