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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.

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Answer:

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

Step-by-step explanation:

137^2-105^2=88^2

18,769-11,025=7,744

88*88=7,744

Answer:

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

Step-by-step explanation:

The hypothenuse is 137 units.

One legt is 105.

Using Pythagorean's Theorem, we have

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

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.

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