The sides of a triangle have lengths 2x + 2, 4x, and 5x + 1. The longest side of the triangle has a length of 5x + 1. For what values of x is the triangle obtuse?

Step-by-step explanation:

(5x+1) ²> (2x+2) ² + (4x) ²

25x²+10x+1>4x²+8x+4+16x²

5x²+2x-3>0

5x²+5x-3x-3>0

5x (x+1) - 3 (x+1) >0

(x+1) (5x-3) >0

x+1=0, gives x=-1

5x-3=0, gives x=3/5

x >0 (because 4x should be >0)

side is always positive.

so x>3/5

again 5x+1<2x+2+4x

5x-6x<2-1

-x<1

x>-1

x=all real values >3/5