Sum

Side of a triangle is given, determine it is a right triangle.

`(2a – 1) cm, 2\sqrt { 2a } cm, and (2a + 1) cm`

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#### Solution

Let p = (2a – 1) cm, `q = 2\sqrt { 2a }` cm and r = (2a + 1) cm.

Then,

`(p^2 + q^2 ) = (2a – 1)^2 cm^2 + (2 )^2 cm^2`

`= {(4a^2 + 1– 4a) + 8a}cm^2`

= (4a^{2} + 4a + 1)cm^{2}

`= (2a + 1)^2 cm^2 = r^2 .`

`(p^2 + q^2 ) = r^2 .`

Hence, the given triangle is right angled

Concept: Right-angled Triangles and Pythagoras Property

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