Question

The perimeter of a rectangle is 102 cm. If the length is 15 cm less than twice the width , what are the dimensions?

Answer 1

Let the length be $\ell$ and the width be $w$. Now, write the length in terms of the width. "The length is 15 cm. less than twice the width" in the form of an equation is

$\ell = 2w - 15 cm.$

Let's plug that into the equation for the perimeter now. The perimeter of a rectangle is $2 \ell + 2w$, so the equation for the perimeter of this rectangle is

$2 \ell + 2w = 102 cm.$

Plugging in the length in terms of width and solving for the width, we get

$2(2w - 15 cm.) + 2w = 102 cm.$
$6w - 30 cm. = 102 cm.$
$6w = 132 cm.$
$\bf w = 22 cm.$

To find the length, we just have to plug in the width into the equation we wrote for the length in terms of the width:

$\ell = 2w + 15 cm.$
$\ell = 2(22 cm.) - 15 cm.$
$\bf \ell = 29 cm.$