To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can use 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.
First, identify the longest side, which is 75 in this case. We'll need to check if the following equation holds:
\[ 75^2 = 60^2 + 45^2 \]
Calculating each term:
- \( 75^2 = 5625 \)
- \( 60^2 = 3600 \)
- \( 45^2 = 2025 \)
Now, summing the squares of the two shorter sides:
\[ 60^2 + 45^2 = 3600 + 2025 = 5625 \]
Now we can compare:
\[ 75^2 = 5625 \] \[ 60^2 + 45^2 = 5625 \]
Since both sides are equal, we can conclude that the triangle with sides measuring 60, 75, and 45 is indeed a right triangle.
The correct answer is: Yes, because 5,625 equals 5,625.
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