To determine whether 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 other two sides.
First, we identify the longest side, which is 75. We will check if the following equation holds:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse (75), and \( a \) and \( b \) are the other two sides (60 and 45):
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Calculate \( c^2 \): \[ 75^2 = 5625 \]
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Calculate \( a^2 + b^2 \): \[ 60^2 + 45^2 = 3600 + 2025 = 5625 \]
Now, we can compare the two results:
- \( c^2 = 5625 \)
- \( a^2 + b^2 = 5625 \)
Since \( 5625 = 5625 \), it confirms that the triangle is a right triangle.
Thus, the answer is: Yes, because 5,625 equals 5,625.
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