Question

How do you find the leg of an isosceles right triangle?

Answer 1

x = unknown leg

h = hypotenuse

Use the pythagorean theorem to do the following.

`a^2+b^2 = c^2\\\\\text{x}^2+\text{x}^2 = \text{h}^2\\\\2\text{x}^2 = \text{h}^2\\\\\text{x}^2 = \frac{\text{h}^2}{2}\\\\\text{x} = \sqrt{\frac{\text{h}^2}{2}}\\\\\text{x} = \frac{\sqrt{\text{h}^2}}{√(2)}\\\\\text{x} = \frac{\text{h}}{√(2)}\\\\\text{x} = \frac{\text{h}√(2)}{2}\\\\`

So for example, if the hypotenuse is h = 10, the leg length x would be:

`\text{x} = \frac{\text{h}√(2)}{2}\\\\\text{x} = (10√(2))/(2)\\\\\text{x} = 5√(2)\\\\\text{x} \approx 7.0710678\\\\`

Try out other values of h.