# If the area of a rectangle is 39 square feet and it has sides of x-2 and x+8, what is the value of x?

May 3, 2018

$\left(x - 2\right) \left(x + 8\right) = 39$

${x}^{2} + 6 x - 16 - 39 = 0$

${x}^{2} + 6 x - 55 = 0$

$\left(x + 11\right) \left(x - 5\right) = 0$

$x = 5 \quad$ We can skip $x = - 11$ which gives negative sides.

Check: (5-2)(5+8)=(3)(13)=39 quad sqrt

May 3, 2018

The value of $x$ is 5.

#### Explanation:

The area of a rectangle can be determined by the following formula.

$A = l \cdot w$

$l$ stands for length or the longer side.
$w$ stands for width or the shorter side.

Now, we can plug the values we are given into the equation.

$A = \left(x - 2\right) \cdot \left(x + 8\right)$

The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.

$A = {x}^{2} + 8 x - 2 x - 16 = {x}^{2} + 6 x - 16$

Now, we can plug in the given value for the area.

$39 = {x}^{2} + 6 x - 16$

Next, we simplify by moving all terms to one side and factor the equation.

$0 = {x}^{2} + 6 x - 55$

Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.

$0 = \left(x - 5\right) \cdot \left(x + 11\right)$

If the equation ultimately equals zero, either $\left(x - 5\right)$ or $\left(x + 11\right)$ or both equal zero. Therefore, we set each equal to zero to find the value of $x$.

$x - 5 = 0$
$x = 5$

$x + 11 = 0$
$x = - 11$

Since $x$ is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.