Question

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?

Answer 1

To determine for what values of x the triangle is obtuse, we need to use the Pythagorean theorem and the properties of obtuse triangles. Given the lengths of the sides as 2x + 2, 4x, and 5x + 1, with the longest side being 5x + 1, we can set up an equation and solve for the range of values for x.

Step-by-step explanation:

To determine for what values of x the triangle is obtuse, we need to use the Pythagorean theorem and the properties of obtuse triangles. In an obtuse triangle, the square of the longest side is greater than the sum of the squares of the other two sides.

Given the lengths of the sides as 2x + 2, 4x, and 5x + 1, with the longest side being 5x + 1, we can set up the following equation: (5x + 1)^2 > (2x + 2)^2 + (4x)^2.

Simplifying and solving this inequality will give us the range of values for x for which the triangle is obtuse.

Answer 2

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