Choose the one alternative that best completes the statement or answers the question.
-A right triangle has an area of 33 square inches. The square of the hypotenuse is 157. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
A) 3 in. and 22 in.
B) 12 in. and 5.5 in.
C) 6 in. and 11 in.
D) 36 in. and 121 in.

Question

Quizplus · Accepted Answer

The area of a right triangle is given by $ \frac{1}{2} \times \text{base} \times \text{height} = 33 $. The Pythagorean theorem states that the square of the hypotenuse (c^2) equals the sum of the squares of the other two sides (a^2 + b^2). Given c^2 = 157, we need to find two numbers a and b such that $ \frac{1}{2}ab = 33 $ and $ a^2 + b^2 = 157 $. Only the combination of 6 in. and 11 in. satisfies both conditions, making it the correct answer.

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