Question

The length of the hypotenuse of a right triangle is 137 units. The length of one leg of the triangle is 105. Gina wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1372 − 1052 = 18,769 − 11,025 = 7,744 units Which statement best explains whether Gina's step is correct or incorrect?

Answer 1

Answer:

She did not do right.  The answer she got is square of one leg.  She should have taken square root and got answer as 88 units.

Step-by-step explanation:

Given that length of hypotenuse is 137 units.  One leg is 105

As per pythagorean theorem , we have

square of hypotenuse = sum of squares of two legs

Hence square of one leg = square of hypotenuse - square of one leg

Thus what she calculated is square of one leg. this is not the unknown side.

Instead she should have found out the square root of 7744 to get the side length of the leg.

Hence leg size =88 units

Answer 2

A^2 + b^2 = c^2
b^2 = c^2 - a^2
b^2 = 137^2 - 105^2
b^2 = 18769 - 11025
b^2 = 7744
b = sqrt 7744
b = 88

Gina's step is not correct... the length of the unknown leg is not 7744, it is the sqrt of 7744, which is 88