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Question: A triangle has sides with lengths of 8 kilometers, 13 kilometers, and 15 kilometers. Is it a right triangle?

To determine if a triangle with sides of 8 kilometers, 13 kilometers, and 15 kilometers is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Let's label the sides a, b, and c, where 'c' represents the longest side (hypotenuse). In this case: a = 8 km b = 13 km c = 15 km We can plug these values into the Pythagorean theorem equation: a^2 + b^2 = c^2 8^2 + 13^2 = 15^2 64 + 169 = 225 233 = 225 Since 233 is not equal to 225, this triangle is not a right triangle.

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