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

Answer:

b.

Step-by-step explanation:

Answer 2

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$\sqrt{2}$ = 10$\sqrt{5}$ 
divide both sides by $\sqrt{2}$ 
x = 10$\sqrt{5}$ / $\sqrt{2}$ 
x = 10$\sqrt{10}$ /2
x = 5$\sqrt{10}$ 

The length of one leg is 5$\sqrt{10}$