# The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

Dec 9, 2016

The width of the rectangle is $4$ inches.

#### Explanation:

We consider the width of the rectangle as $x$ which will make the length $\left(x + 6\right)$. Since we know the area, and the formula of a rectangle's area to be length $\times$ breadth, we can write:

$x \times \left(x + 6\right) = 40$

Open the brackets and simplify.

${x}^{2} + 6 x = 40$

Subtract $40$ from both sides.

${x}^{2} + 6 x - 40 = 0$

Factorise.

${x}^{2} + 10 x - 4 x - 40 = 0$

$x \left(x + 10\right) - 4 \left(x + 10\right) = 0$

$\left(x - 4\right) \left(x + 10\right) = 0$

$x - 4 = 0$ and $x + 10 = 0$

$x = 4$ and $x = - 10$

The only possibility in the above problem is that $x = 4$.

That will make the width $4$ and the length $\left(x + 6\right)$ which is $10$, and the area $\left(4 \times 10\right)$ which is $40$.