Discussion
Which of the following measurements (in cm) can be the sides of a right triangle ?
Answer: C
The sides 14, 50, 48 form a right triangle.
By Pythagoras, the square of the longest side must equal the sum of the squares of the other two.
\[ \begin{aligned} 14^2 + 48^2 &= 196 + 2304 \\ &= 2500 = 50^2 \end{aligned} \]
The others fail: \(16^2 + 30^2 = 1156\), not \(32^2 = 1024\); \(12^2 + 44^2 = 2080\), not \(50^2 = 2500\); and \(12^2 + 18^2 = 468\), not \(20^2 = 400\). A quick check is that 14, 48, 50 is just 2 times the familiar triple 7, 24, 25.
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