Chapter 6.4, Problem 11CE

To determine

To check: if it possible to have a triangle with given sides

Answer to Problem 11CE

Yes, it is possible to have a triangle with sides equal to $0.6,0.5,1$

Explanation of Solution

Given information: Sides of a triangle are equal to $0.6,0.5,1$

The triangle inequality theorem explains that addition of any two sides from three sides of the triangle must greater in length than the third side.

Sides of a triangle are equal to $0.6,0.5,1$ .

Here,

  $\begin{array}{l}0.6+0.5=1.1>1\\ 0.5+1=1.5>0.6\\ 0.6+1=1.6>0.5\end{array}$

As addition of any two sides of a triangle is greater than the remaining side, it is possible to have a triangle with such sides.