Question

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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

The answer is C It is correct because the length of the unknown side is the difference of the lengths of the sides.

Explanation:

137^2-105^2=88^2

18,769-11,025=7,744

88*88=7,744

Answer 2

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

Explanation:

The hypothenuse is 137 units.

One legt is 105.

Using Pythagorean's Theorem, we have

`a^(2) =b^(2) +c^(2)\\ (137)^(2)=(105)^(2)+c^(2)\\c=\sqrt{(137)^(2)-(105)^(2)} \\c=√(18,769-11,025) =√(7,744)\\ c = 88`

Therefore, Gina's process is uncompleted, because the length of the missing leg is the square root of 7,744, which is 88.

So, the right answer is B.