# How do you find the area of a right triangle if one leg is three times the other and the hypotenuse is 10?

May 27, 2015

Let the shorter leg of the right triangle be $x$
$\rightarrow$ the longer leg is $3 x$

Since the hypotenuse is $10$
by the Pythagorean Theorem

${x}^{2} + {\left(3 x\right)}^{2} = {10}^{2}$

$10 {x}^{2} = 100$

$x = \sqrt{10}$

The area of the triangle is
$A = \frac{1}{2} b h$

$= \frac{1}{2} \cdot \sqrt{10} \cdot 3 \left(\sqrt{10}\right)$

$= 15$