To determine if the triangle with sides measuring 60, 75, and 45 is a right triangle, we can apply the Pythagorean theorem, which 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 sides: Here, the sides are 60, 75, and 45. The longest side is 75.
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Calculate the squares of the sides:
- \( 75^2 = 5625 \)
- \( 60^2 = 3600 \)
- \( 45^2 = 2025 \)
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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, we can conclude that:
Yes, because 5,625 equals 5,625.