Question

In a triangle, if the sum of two sides is x and their product is y such that (x + z) (x – z) = y where z is the third side of the triangle then the triangle is

• A. Equilateral
• B. Tight angled
• C. Obtuse angled
• D. None of these

Answer 1

Answer: (C)

Obtuse angled

Answer 2

Let ABC be the triangle with b + c = x and

bc = y then a = z, and from the given relations we have

(b + c + a) (b + c – a) = bc

Ž b² + c² – a² = – bc

Ž $\frac { b ^ { 2 } + c ^ { 2 } - a ^ { 2 } } { 2 b c } = - \frac { 1 } { 2 }$

Ž cos A = – $\frac { 1 } { 2 }$= cos 120⁰

Ž A = 120⁰ and the triangle is obtuse angled.

Ž A is an obtuse angle.