Chapter 8, Problem 6CUR

To determine

The statement in the given question

Answer to Problem 6CUR

The final answer is $-1<x<5$

Explanation of Solution

Given information:

The sides of obtuse triangle are x, 2x+2, 2x+3.

Let ABC be a triangle

Also let a=x, b=2x+2 and c=2x+3

Where c is the largest side

In obtuse angle triangle

  $\begin{array}{c}{c}^2>a^2+b^2\\ {\left(2x+3\right)}^2>{\left(x\right)}^2+{\left(2x+2\right)}^2\\ 4x^2+12x+9>x^2+4x^2+8x+4\\ x^2-4x-5<0\\ x^2+x-5x-5x<0\\ x\left(x+1\right)-5\left(x+1\right)<0\\ \left(x+1\right)\left(x-5\right)<0\\ -1<x<5\end{array}$

Therefore, the side of an obtuse triangle having length x, 2x+2, 2x+3, the value of x always lies $-1<x<5$