Question

If the legs of a right triangle are given by x^2 - y^2 and 2xy then which expression equals the hypotenuse ? Choose all that apply

Answer 1

`√(\left(x^2-y^2\right)^2+\left(2xy\right)^2)`

Explanation:

Hypotenuse of a right triangle can be found using the Pythagorean theorem which states that both legs squared and added is equal to the hypotenuse squared. In other words, if A and B are legs and C is the hypotenuse:

`C=√(A^2+B^2)`

We are told that one of the legs is
`x^2-y^2` and the other is
`2xy` so we get
`√(\left(x^2-y^2\right)^2+\left(2xy\right)^2)` when we substitute the legs into the formula presented above.