# The length of a rectangle is 8cm greater than its width. How do you find the dimensions of the rectangle if its area is 105cm²?

Apr 1, 2018

Dimensions: $15$cm $\times$ $7$ cm

#### Explanation:

Let the length of the rectangle be $l$ and the width of the rectangle be $w$,

$l \cdot w = 105$

$l = w + 8$

Substitute $l = w + 8$ into $l \cdot w = 105$,

$\left(w + 8\right) \cdot w = 105$

Expand,

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

Factor,

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

Solve,

w=7 or cancel(-15 ( reject $- 15$ as $w > 0$ )

When $w = 7$,

$l = 7 + 8$
$l = 15$

Hence, the length is $15$cm and the width is $7$cm.