# If the length of a rectangle is (x+4) and the width of the rectangle is (x+1) and the area of the rectangle is 100, what does x equal?

Jun 21, 2016

$x = 7.612$

#### Explanation:

Here, the length of a rectangle is $\left(x + 4\right)$ and the width of the rectangle is $\left(x + 1\right)$ and the area of the rectangle is $100$.

Hence as area is product of length and width, we have

$\left(x + 4\right) \left(x + 1\right) = 100$ or

${x}^{2} + 4 x + x + 4 = 100$ or

${x}^{2} + 5 x - 96 = 0$

as discriminant is ${5}^{2} - 4 \cdot 1 \cdot \left(- 96\right) = 25 + 384 = 409$ is not the square of a rational number, we will have to use quadratic formula and

$x = \frac{- 5 \pm \sqrt{409}}{2} = \frac{- 5 \pm 20.224}{2}$ i.e.

$x = 7.612$ or $x = - 12.612$

But as length cannot be negative, $x = 7.612$