CPM Homework Help : CCG Problem 5-127

A right triangle with both legs = to X, and hypotenuse of 16. Examine the triangle shown at right. Solve for $x$ twice, using two different methods. Show your work for each method clearly.

Hint:

This triangle is similar to a $45º\text{-}45º\text{-}90º$ special right triangle.

More Help:

A second way to solve for $x$ would be to use the Pythagorean Theorem.

Answer:

Using the Pythagorean Theorem you get $x^2+x^2=16^2$
Combine like terms you get $2x^2=256$ .
Solve for $x$ and simplify your radical.

$x=8\sqrt{2}$