# The height of a triangle is four times the length of the base. What is the base and height of the triangle if the area is 18 square inches?

Dec 19, 2015

$\textcolor{w h i t e}{\times} a = 3$ and $h = 12$

#### Explanation:

Let height be h, base be a, and area be A:

$\textcolor{w h i t e}{\times} h = 4 a$

$\textcolor{w h i t e}{\times} \frac{a h}{2} = A$ $\textcolor{w h i t e}{\times \times \times \times \times \times x}$(area formula)
$\implies \frac{\textcolor{red}{4 {a}^{2}}}{2} = \textcolor{red}{18}$
$\implies \textcolor{red}{\frac{1}{2} \times} \frac{4 {a}^{2}}{2} = \textcolor{red}{\frac{1}{2} \times} 18$

Take the squareroot of both sides:
$\implies \sqrt{{a}^{2}} = \sqrt{9}$
$\implies a = 3$

$\textcolor{w h i t e}{\times} h = 4 \times 3$
$\textcolor{w h i t e}{\times x} = 12$