What is length of hypotenuse if height and base is 50 and 150?

I assume you’re dealing with a right triangle in this problem, in which case we should use the Pythagorean Theorem to find the length of our missing hypotenuse. You might remember from geometry that the Pythagorean theorem states that, for a right triangle with legs a and b and hypotenuse c:

a^2 + b^2 = c^2

(I’ve attach a proof of this fact – and a proof I personally find incredibly beautiful – with this response)

If our legs here are 50 and 150, then we know that

50^2 + 150^2 = c^2

Which becomes

2500 + 22500 = c^2
25000 = c^2

Finally, taking the square root of both sides gets us

c = 50 * sqrt(10)

Which is about as simplified as we can get it.