Question

The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 − 1322 = 24,649 − 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect?

It is correct because the length of the unknown side is the difference of the lengths of the sides.
It is correct because the length of the unknown side is the difference of the squares of the sides.
It is incorrect because the length of the unknown side is the square root of 42,073.
It is incorrect because the length of the unknown side is the square root of 7,225.

Answer 1

It is correct because the length of the unknown side is the difference of the squares of the sides.

Answer 2

It is incorrect because the length of the unknown side is the square root of 7,225.

If you use the pythagorean theorem and plug in the values,

a^2 + 132^2 = 157^2

a^2 + 17424 = 24649
-17424 -17424
_________________
a^2 = 7225

If you square root it, the final answer would be 85.