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