SOLUTION: I have a 45 45 90 degree triangle and one leg is 5(square root of)2. I have to find the length of the hypotenuse. I don't know what to do. Thank you!

Question 246874: I have a 45 45 90 degree triangle and one leg is 5(square root of)2. I have to find the length of the hypotenuse. I don't know what to do. Thank you!
Found 2 solutions by richwmiller, solver91311:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
This is a right triangle and also an isosceles triangle. Two legs and angles are equal)
the formula for the hypotenuse is a^2+b^2=c^2
both a and b are the same
2*(5sqrt2)^2=c^2
2*25*2=c^2
You should be able to finish this

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are a couple of ways to go about this.

First thing you could do is recognize that a 45 45 90 triangle is an isosceles right triangle. That means that both legs are the same length. Use the Pythagorean theorem:

Or you could remember that the sides of a 45 45 90 triangle are always in proportion:

So just multiply by

John

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