# How do you find the third side of a right triangle if the base is x = 20m, and height is y = 20m?

Jun 6, 2015

The third side is the hypotenuse, which is $20 \sqrt{2} \text{m}$.

This is an example of an iscoseles right triangle, in which the angles are 45-45-90 degrees. In an iscoseles right triangle, the base and height are the same. The hypotenuse is the missing side and is equal to $\text{L} \sqrt{2}$, where $\text{L}$ refers to either of the other two legs, which are equal. Therefore, the length of the hypotenuse is $20 \sqrt{2} \text{m}$.

We can use the Pythagorean theorem to prove this: ${c}^{2} = {a}^{2} + {b}^{2}$. Let side $x = a = 20 \text{m}$ and side $y = b = 20 \text{m}$. The hypotenuse is $c$.

${c}^{2} = {\left(20 \text{m")^2+(20"m}\right)}^{2}$ =

${c}^{2} = 400 {\text{m"^2+400"m}}^{2}$

${c}^{2} = 800 \text{m"^2}$

$c = \sqrt{800 {\text{m}}^{2}}$ =

$c = \sqrt{20 \times 20 \times 2 \times {\text{m}}^{2}}$ =

$c = 20 \sqrt{2} \text{m}$