To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can apply the Pythagorean theorem. For a triangle to be a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side.
Here are the side lengths:
- a = 45
- b = 60
- c = 75 (the longest side)
Now we check the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Calculating:
- \( 45^2 = 2025 \)
- \( 60^2 = 3600 \)
- \( 75^2 = 5625 \)
Now, add the squares of the shorter sides:
\[ 2025 + 3600 = 5625 \]
Since \( 5625 = 5625 \), this means that
\[ 45^2 + 60^2 = 75^2 \]
Therefore, the triangle is a right triangle.
The correct response is: Yes, because 5,625 equals 5,625.
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