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

Solution

## The correct option is C Obtuse angleLet $$a=3x+4y,b=4x+3y,c=5x+5y$$, clearly $$c$$ is the largest side and thus the largest angle $$C$$ is given by$$\cos { C } =\cfrac { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }{ 2ab } =\cfrac { -2xy }{ 2\left( 12{ x }^{ 2 }+25xy+12{ y }^{ 2 } \right) } <0$$$$\Rightarrow cos C$$ is negative and only the angles which have greater than 90 value have the cos as negative. Hence the triangle is obtuse triangle.Mathematics

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