Discussion
The sides of four triangles are given in the options.
Which of them forms a right triangle ?
Answer: C
The right triangle is (iii), with sides 11 cm, 60 cm and 61 cm.
By the converse of Pythagoras' theorem, a triangle is right-angled when the square of the longest side equals the sum of the squares of the other two:
\[ \begin{aligned} 11^{2} + 60^{2} &= 121 + 3600 = 3721 \\ 61^{2} &= 3721 \end{aligned} \]
The others fail: \(20^{2} + 22^{2} = 884 \ne 576\); \(15^{2} + 32^{2} = 1249 \ne 1369\); \(19^{2} + 40^{2} = 1961 \ne 1681\). The familiar triple 9, 40, 41 has 9, not 19, so (iv) is a near miss.
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