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A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.
Yes, the triangle with side lengths 6, 8, and 10 is a right triangle. This can be proven using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 10, and the other two sides are 6 and 8. We can check if the Pythagorean theorem holds true by plugging in the values:
10^2 = 6^2 + 8^2
100 = 36 + 64
100 = 100
Since the equation is true, it confirms that the triangle is a right triangle.