Answer: m = 7
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Explanation:
For any 45-45-90 triangle, the two legs are the same length.
So m = n.
This is because the two angles opposite these legs are congruent.
Using the Pythagorean theorem, we can find m
m^2+n^2 = (7*sqrt(2))^2
m^2+m^2 = 98
2m^2 = 98
m^2 = 98/2
m^2 = 49
m = sqrt(49)
m = 7
As a quick shortcut, the hypotenuse of any 45-45-90 triangle is always sqrt(2) times the leg.
hypotenuse = (leg)*sqrt(2)
