Question

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

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

Answer 1

The correct option is C Obtuse angled

Sides are $3x+4y,4x+3y$ and $5x+5y$ units, $x,y>0$

We have,

$a^2={(3x+4y)}^2=9x^2+16y^2+24xy{b}^2={(4x+3y)}^2=16x^2+9y^2+24xy{c}^2={(5x+5y)}^2=25x^2+25y^2+50xy$

$\therefore a^2+b^2-c^2=-2xy<0$ as $x>0,y>0$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$ $=\frac{-2xy}{2(3x+4y)(4x+3y)}$

$\Rightarrow \cos C<0$

$\Rightarrow C$ must be obtuse angle