Question

What is the length of leg y of the right triangle?

Answer 1

y = 13

Explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

y² + 84² = 85²

y² + 7056 = 7225 ( subtract 7056 from both sides )

y² = 169 ( take the square root of both sides )

y =
`√(169)` = 13

Answer 2

13

Explanation:

We need to use the Pythagorean Theorem to solve this problem:

`a^(2) +b^(2) = c^(2)` , where a and b are the legs of the right triangle and c is the hypotenuse

In this case, we already know b (b = 84) and c (c = 85), so we need to solve for a:

`a^(2) = c^(2) - b^(2) = 85^(2) - 84^(2) = 169 = 13^(2)`

Thus, a = y = 13.