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A triangle with sides of lengths 32, 60, and 68 is a right triangle.A.TrueB.False

Question

A triangle with sides of lengths 32, 60, and 68 is a right triangle.A.TrueB.False

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Solution

The statement is True. This is because the triangle follows the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as: a² + b² = c².

In this case, if we consider 32 and 60 as the two sides (a and b), and 68 as the hypotenuse (c), we can substitute these values into the theorem:

32² + 60² = 68² 1024 + 3600 = 4624 4624 = 4624

Since both sides of the equation are equal, the triangle with sides of lengths 32, 60, and 68 is indeed a right triangle.

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