Question

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y units, where x, y > 0. The triangle is

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

Answer 1

Answer: (C)

Obtuse angled

Answer 2

Let a = 3x + 4y, b = 4x + 3y and C = 5x + 5y.

Clearly c is the largest side and then the largest angle C is given by

cos C = $\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }$= $\frac { - 2 x y } { 2 \left( 12 x ^ { 2 } + 25 x y + 12 y ^ { 2 } \right) } < 0$.

⇒ C is an obtuse angle