#### 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, AB^{2} = (a − 1)2 = a2 + 1 − 2𝑎

BC^{2} = (2`sqrta`)^{2} = 4a

CA^{2} = (a + 1)^{2} = a^{2} + 1 + 2a

Hence AB^{2} + BC^{2} = AC^{2}

So Δ ABC is right angled Δ at B.

Is there an error in this question or solution?

#### APPEARS IN

Solution Determine Whether the Triangle Having Sides (A − 1) Cm, 2`Sqrta` Cm and (A + 1) Cm is a Right-angled Triangle. Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle.