1 Answer

Varda · Answer 1 · 2016-10-31T18:48:08+0000

Let the length be
$\ell$ and the width be

. 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.

$\bf w = 22 cm.$

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:

$\ell = 2w + 15 cm.$

$\ell = 2(22 cm.) - 15 cm.$

$\bf \ell = 29 cm.$

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