Question

The sides of a triangle are 3x+4y, 4x+3y, 5x+5y where x,y>0 then Triangle is

1.Right angle

2.Obtuse angle

3.Equilateral

4.None of the above

Answer 1

Sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y units. And x > 0 and y > 0
Let a = 3x + 4y , b = 4x + 3y and c = 5x + 5y
Here a ,b and c are length of the sides.

So after observation c is the longest side .

So cosC = b2+a2−c22ab =(3x +4y)2 +(4x +3y )2−(5x+5y )22(3x+4y)(4x+3y) =−2xy2(3x+4y)(4x+3y)

So cosC is negative , And only the angles which have greater then 90 value have cos as negative .
Hence the triangle is obtuse triangle.