To determine which of the given sets could represent the sides of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \):
\[ a^2 + b^2 = c^2 \]
Let's evaluate each option:
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2, 2, and 5:
- \( 2^2 + 2^2 = 4 + 4 = 8 \)
- \( 5^2 = 25 \)
- Not a right triangle.
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1.5, 2.5, and 4:
- \( 1.5^2 + 2.5^2 = 2.25 + 6.25 = 8.5 \)
- \( 4^2 = 16 \)
- Not a right triangle.
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2, 3, and 5:
- \( 2^2 + 3^2 = 4 + 9 = 13 \)
- \( 5^2 = 25 \)
- Not a right triangle.
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2.5, 6, and 6.5:
- \( 2.5^2 + 6^2 = 6.25 + 36 = 42.25 \)
- \( 6.5^2 = 42.25 \)
- This is a right triangle.
The correct answer is 2.5, 6, and 6.5.