# Length of a rectangle exceeds its width by 12 inches and its area is 768 square inches. Write the equation which solves this problem?

Dec 7, 2016

The desired quadratic equation is ${w}^{2} + 12 w - 768 = 0$

#### Explanation:

Let the width of the rectangular window be $w$ inches.

As length exceeds width by $12$ inches, it s $w + 12$ inches.

Hence area is $w \left(w + 12\right)$ and as it is $768$ square inches, we have

$w \left(w + 12\right) = 768$

or ${w}^{2} + 12 w = 768$

or ${w}^{2} + 12 w - 768 = 0$