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?

A. It is incorrect because the length of the unknown side is the square root of 29,794.
B. It is incorrect because the length of the unknown side is the square root of 7,744.
C. It is correct because the length of the unknown side is the difference of the lengths of the sides.
D. It is correct because the length of the unknown side is the difference of the squares of the sides

Answer 1

it is incorrect because the length of the unknown side is the square root of 7,744.

Explanation:

a^2 + b^2 = c^2

105^2+ b^2 = 137^2

11025+ b^2= 18769

11025-11025+ b^2 = 18769-11025

b^2= 7704

sqr b^2= sqr 7704

b=87.77243303

b=87.8 simplified

therefore,this gina is wrong because the lenght of the unknown leg is the square root of 7,744.

hope it helps.

Answer 2

B. It is incorrect because the length of the unknown side is the square root of 7,744

Explanation:

Given

• a = 137
• b = 105
• c = ?

Solution

As per Pythagorean theorem:

• c² = a² - b²
• c² = 137² - 105² = 18769 - 11025 = 7744
• c = √7744 = 88 units

Gina's incorrect step is:

• B. It is incorrect because the length of the unknown side is the square root of 7,744