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Question
Determine whether the triangle having sides (a − 1) cm, 2`sqrta` cm and (a + 1) cm is a right-angled
triangle.
Solution
Let ABC be the Δ with
AB = (a – 1) cm BC = 2`sqrta` cm, CA = (a + 1) cm
Hence, AB2 = (a − 1)2 = a2 + 1 − 2𝑎
BC2 = (2`sqrta`)2 = 4a
CA2 = (a + 1)2 = a2 + 1 + 2a
Hence AB2 + BC2 = AC2
So Δ ABC is right angled Δ at B.
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