Question

Ms. Green tells you that a right triangle has a hypotenuse if 13 and a leg of 5. She ask you to find the other leg of the triangle. What is you're answer?

Answer 1

`{x}^(2) + {5}^(2) = {13}^(2) \: \: \\ by \: the \: pythagorean \: theorem \\ \\ {13}^(2) - {5}^(2) = 169 - 25 \\ = 144 = {x}^(2) = {12}^(2) \\ so \: x = 12`

Answer 2

The other leg is 12

Explanation:

We can use the Pythagorean theorem to solve this problem.

a^2+b^2 = c^2

The legs are a and b and the hypotenuse is c

5^2 +b^2 = 13^2

25 + b^2 = 169

Subtract 25 from each side

25-25 +b^2 = 169-25

b^2 = 144

Take the square root of each side

sqrt(b^2) = sqrt(144)

b= 12