Question
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A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.
(2 points)
Yes, the triangle with side lengths of 6, 8, and 10 is a right triangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using the Pythagorean theorem, we can calculate:
6^2 + 8^2 = 36 + 64 = 100
Since the sum of the squares of the lengths of the other two sides (36 + 64) equals the square of the length of the hypotenuse (100), the triangle satisfies the Pythagorean theorem and is therefore a right triangle.