To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we need to use the Pythagorean theorem. The Pythagorean theorem states that in 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.
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Identify the longest side: The longest side here is 75.
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Calculate the squares of the sides:
- \(60^2 = 3600\)
- \(75^2 = 5625\)
- \(45^2 = 2025\)
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Check the Pythagorean theorem: \[ 75^2 \stackrel{?}{=} 60^2 + 45^2 \] \[ 5625 \stackrel{?}{=} 3600 + 2025 \] \[ 5625 \stackrel{?}{=} 5625 \]
Since both sides of the equation are equal, the triangle with sides 60, 75, and 45 is indeed a right triangle.
The correct response is: Yes, because 5,625 equals 5,625.