To determine whether the triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. For a triangle to be a right triangle, the following must hold true:
\( c^2 = a^2 + b^2 \)
where \( c \) is the length of the longest side (the hypotenuse) and \( a \) and \( b \) are the lengths of the other two sides.
In this case, the lengths are:
- \( a = 45 \)
- \( b = 60 \)
- \( c = 75 \) (the longest side)
Now we calculate:
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Calculate \( c^2 \): \[ c^2 = 75^2 = 5625 \]
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Calculate \( a^2 + b^2 \): \[ a^2 + b^2 = 45^2 + 60^2 = 2025 + 3600 = 5625 \]
Now we compare \( c^2 \) and \( a^2 + b^2 \): \[ 5625 = 5625 \]
Since they are equal, the triangle with sides measuring 60, 75, and 45 is a right triangle.
Thus, the correct statement is: Yes, because 5,625 equals 5,625.