Question
A triangle has side lengths of 24 in., 32 in., and 40 in. Is the triangle acute, obtuse, or right?
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GPT 3.5
In this case, we can use the Pythagorean theorem to determine whether the triangle is acute, obtuse, or right.
If a triangle is a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, 40^2 = 1600, 24^2 = 576, and 32^2 = 1024.
By comparing these values, we can see that 1024 + 576 = 1600, which means that the triangle with side lengths of 24 in., 32 in., and 40 in. is a right triangle.
If a triangle is a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, 40^2 = 1600, 24^2 = 576, and 32^2 = 1024.
By comparing these values, we can see that 1024 + 576 = 1600, which means that the triangle with side lengths of 24 in., 32 in., and 40 in. is a right triangle.
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