# The length of a rectangle is 8 cm greater than the width. The area of the rectangle is 105 cm 2. How do you find the width and the length?

Oct 19, 2016

Let $x$ be the width of the rectangle and $x + 8$ be the length.

$A = l \times w$

$105 = x \left(x + 8\right)$

$105 = {x}^{2} + 8 x$

$0 = {x}^{2} + 8 x - 105$

$0 = \left(x + 15\right) \left(x - 7\right)$

$x = - 15 \mathmr{and} 7$

Since a negative length is impossible, the rectangle measures 7 centimetres by $15$ centimetres.

Hopefully this helps!