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.`