# The hypotenuse of a right angled triangle is of length square root34. The sum of the other two sides is 8. How do you find the length of each side?

Feb 12, 2016

I found $3 \mathmr{and} 5$

#### Explanation:

We can use Pythagoras theorem where $a$ and $b$ are the two sides and $c = \sqrt{34}$ is the hipotenuse to get:
${c}^{2} = {a}^{2} + {b}^{2}$
you also know that $a + b = 8$
or $a = 8 - b$ into ${c}^{2} = {a}^{2} + {b}^{2}$ you get:
$34 = {\left(8 - b\right)}^{2} + {b}^{2}$
$34 = 64 - 16 b + {b}^{2} + {b}^{2}$
$2 {b}^{2} - 16 b + 30 = 0$
Using the Quadratic Formula:
${b}_{1 , 2} = \frac{16 \pm \sqrt{256 - 240}}{4} = \frac{16 \pm 4}{4}$
getting:
${b}_{1} = 5$
${b}_{2} = 3$
and:
${a}_{1} = 8 - 5 = 3$
${a}_{2} = 8 - 3 = 5$