# One side of a rectangle is twice the length of the other. The area is 100. What are the dimensions?

Jun 10, 2016

$\textcolor{b l u e}{\implies L = 5 \sqrt{2}} \text{ "larr" shorter sides}$

$\textcolor{b l u e}{\implies 2 L = 10 \sqrt{2}} \text{ "larr" longer side}$

#### Explanation:

Let the shorter side length be $L$

Then the longer side length is $2 L$

Thus given area $= 100 = \left(2 L\right) \times \left(L\right)$

$\implies 2 {L}^{2} = 100$

Divide both sides by 2 giving

$\frac{2}{2} {L}^{2} = \frac{100}{2}$

But $\frac{2}{2} = 1 \text{ and } \frac{100}{2} = 50$

${L}^{2} = 50$

Square root both sides

$\sqrt{{L}^{2}} = \sqrt{50}$

But $\text{ "50" " =" " 10xx5" " =" " 2xx5xx5" " =" } 2 \times {5}^{2}$

$\implies L = \sqrt{2 \times {5}^{2}}$

$\textcolor{b l u e}{\implies L = 5 \sqrt{2}} \text{ "larr" shorter sides}$

$\textcolor{b l u e}{\implies 2 L = 10 \sqrt{2}} \text{ "larr" longer side}$