Question

Determine whether the triangle, the lengths of whose sides are 3cm,4cm,5cm is a right-angled triangle​

Answer 1

Step-by-step explanation:

Triangle having sides (a - 1) cm, 2√a and (a + 1) cm.  

Let ABC be the triangle in which with the sides are  AB = (a - 1)cm ,  BC = (2√ a) cm, CA = (a + 1) cm  

Hence, AB² = (a -1)²  = a² + 1² -2×a×1  

[(a- b)² = a²+b² - 2ab]

AB² = a² + 1 -2a

BC² = (2√ a)²

BC = 4a

CA² = (a + 1)²  = a² + 1² + 2×a×1  

[(a + b)² = a²+b² + 2ab]

CA² = a² + 1 + 2a

AC² = AB² + BC²

[By pythagoras theorem]

a² + 1 + 2a = a² + 1 - 2a + 4a

a² + 1 + 2a = a² + 1 + 2a

Hence, AC² = AB² + BC²

This proves that ∆ABC is right angled ∆ at B.

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