Question

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

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

Answer 1

The correct option is C Obtuse angle

Let $a=3x+4y,b=4x+3y,c=5x+5y$, clearly $c$ is the largest side and thus the largest angle $C$ is given by
$\cos C=\frac{a^2+b^2-c^2}{2ab}=\frac{-2xy}{2(12x^2+25xy+12y^2)}<0$
$\Rightarrow cosC$ is negative and only the angles which have greater than 90 value have the cos as negative.

Hence the triangle is obtuse triangle.