Discussion
Which of the following measurements (in cm) cannot form the sides of a right triangle?
Answer: D
The set that cannot form a right triangle is 8, 16, 12.
Three lengths form a right triangle only when the square of the longest equals the sum of the squares of the other two (the converse of Pythagoras' theorem).
\[ \begin{aligned} 8^{2} + 12^{2} &= 64 + 144 = 208 \\ 16^{2} &= 256 \ne 208 \end{aligned} \]
The other sets pass: \(2.5^{2} + 6^{2} = 6.25 + 36 = 42.25 = 6.5^{2}\); \(12^{2} + 16^{2} = 400 = 20^{2}\); and \(4.5^{2} + 6^{2} = 20.25 + 36 = 56.25 = 7.5^{2}\).
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