1.

The sides of certain triangles are (a – 1) cm, 2√a cm, (a + 1) cm. Determine of are right triangles.

Answer»

A given triangle to be right-angled, if it satisfies Pythagorean Theorem. That is, the sum of the squares of the two smaller sides must be equal to the square of the largest side.

(a- 1) cm, 2√a cm, (a + 1) cm

Longest side = (a + 1) cm

(a + 1)2 = a2 + 2a + 1

and (a – 1)2 + (2 √a )2 = a2 – 2a + 1 + 4a = a2 + 2a + 1

a2 + 2a + 1 = a2 + 2a + 1

It is a right triangle.



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