Discussion
Which of the following can be the sides of a right angled triangle ?
Answer: D
The sides 65 cm, 72 cm and 97 cm can form a right angled triangle.
A triangle is right angled exactly when the square of the longest side equals the sum of the squares of the other two (the converse of Pythagoras' theorem).
\[ \begin{aligned} 65^{2} + 72^{2} &= 4225 + 5184 \\ &= 9409 = 97^{2} \end{aligned} \]
The others fail: \(20^{2} + 21^{2} = 841 = 29^{2}\), not \(31^{2}\); \(35^{2} + 77^{2} = 7154\), not \(88^{2} = 7744\); and 15, 32, 57 cannot even form a triangle, since \(15 + 32 \lt 57\).
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