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

The correct option is C obtuse angled

Let $a=3x+4y,b=4x+3y$ and $c=5x+5y$ be the largest side

$\Rightarrow \cos C=\frac{a^2+b^2-c^2}{2ab}$

$=\frac{{(3x+4y)}^2+{(4x+3y)}^2-{(5x+5y)}^2}{2(3x+4y)(4x+3y)}$

$\Rightarrow \cos C=\frac{9x^2+16y^2+24xy+16x^2+9y^2+24xy-25x^2-25y^2-50xy}{2(3x+4y)(4x+3y)}<0,x,y>0$

$\Rightarrow \cos C=\frac{-2xy}{2(3x+4y)(4x+3y)}<0,x,y>0$

$\Rightarrow \theta >{90}^{\circ }$

$\therefore ,$ the triangle is obtuse angled.