if you have a right triangle where the sum of the square of all three sides is 200. What is the hypotenuse?

Answer 1

a² + b² = h²
a² + b² + h² = 200
h² + h² = 200
2h² = 200
h² = 100
h = 10

The hypotenuse is 10 units.

Answer 2

If the sides are a, b, and c, with c the hypotenuse, then we have a² + b² = c². In addition, we're told that a² + b² + c² = 200. So

200 = (a² + b²) + c² = c² + c² = 2c²

So c²=100 and so c=10

Answer 3

you know that for a right triangle that a^2 + b^2 = c^2

Your problem says that a^2 + b^2 + c^2 = 200
substitute c^2 in for the a^2 + b^2 because of pythag. theorem

c^2 + c^2 = 200
2c^2 = 200
c^2 = 100
c = 10

Answer 4

a^2 + b^2 = c^2
a^2 + b^2 + c^2 = 200
c^2 + c^2 = 200
2c^2 = 200
c^2 = 100
c = 10