# Inside that rectangle, there is a smaller one. It has a width of 2x and a length of x + 12. How do you find the area?

Apr 15, 2016

$2 {x}^{2} + 24$

#### Explanation:

Recall that the formula for area of a rectangle is:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} A = l w \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$A =$area of rectangle
$l =$length
$w =$width

To determine the area of the rectangle, substitute the given expressions for the length and width into the formula for the area of a rectangle.

$A = l w$

$A = \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{x} + \textcolor{b l u e}{12}\right) \left(\textcolor{red}{2 x}\right)$

Use the distributive property, $\textcolor{red}{a} \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{b} + \textcolor{b l u e}{c}\right) = \textcolor{red}{a} \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{b} + \textcolor{red}{a} \textcolor{b l u e}{c}$, to simplify the equation.

$A = \left(\textcolor{red}{2 x}\right) \left(\textcolor{\mathmr{and} a n \ge}{x}\right) + \left(\textcolor{red}{2 x}\right) \left(\textcolor{b l u e}{12}\right)$

$A = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 2 {x}^{2} + 24 x \textcolor{w h i t e}{\frac{a}{a}} |}}}$