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.