Question

The hypotenuse of a 45°-45°-90° triangle measures 10 sqrt 5 in. What is the length of one leg of the triangle?

Answer 1

There is this specific ratio for 45-45-90 triangles where the length of the hypotenuse is radical 2 times as long as a leg. With this in mind, we can create an equation where the length of one leg is represented with the variable x.

x
`√(2)` = 10
`√(5)`
divide both sides by
`√(2)`
x = 10
`√(5)` /
`√(2)`
x = 10
`√(10)` /2
x = 5
`√(10)`

The length of one leg is 5
`√(10)`