CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
Equilateral
loader
C
Obtuse angle
loader
D
None of these
loader

Solution

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
$$\cos { C } =\cfrac { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } }{ 2ab } =\cfrac { -2xy }{ 2\left( 12{ x }^{ 2 }+25xy+12{ y }^{ 2 } \right)  } <0$$
$$\Rightarrow cos C$$ is negative and only the angles which have greater than 90 value have the cos as negative.

Hence the triangle is obtuse triangle.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image