# The hypotenuse of an isosceles right triangle is 8.4 in. How do you find the length of a side to the nearest tenth of an inch?

##### 1 Answer
Nov 3, 2015

The length of the side is $a \approx 5.9$ inch

#### Explanation:

According to the Pythagorean Theorem we have:

${a}^{2} + {b}^{2} = {c}^{2}$

Since the triangle is isosceles and the hypotenuse is given, you can write it as:

${a}^{2} + {a}^{2} = {8.4}^{2}$

$2 {a}^{2} = {8.4}^{2}$

${a}^{2} = {\left(8.4\right)}^{2} / 2$

${a}^{2} = \frac{70.56}{2}$

${a}^{2} = 35.28$

$a \approx 5.9$