The two legs (labeled x) of the right triangle below have equal length. If the hypotenuse has length 5√2, solve for x.

x=5

Step-by-step explanation:

Other than using the plain special aspect of a 45-45-90 triangle where the legs are x, x, and x√2, you can solve for this.

Since the two legs have equal length, they are both x. Using the pythagorean theorem:

(x^2) + (x^2) = 50 (Because 5 squared is 25 and √2 squared is 2, multiplying them gives you 50).

You can add (x^2) and (x^2) because they are the same terms (x squared).

Simplifying like so gives you:

2x^2=50

Dividing by two on both sides:

x^2=25

Taking the square root of both sides:

x=5