Chapter 6.4, Problem 7CE

To determine

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

Answer to Problem 7CE

Yes, it is possible to have a triangle with sides equal to $10,9,8$

Explanation of Solution

Given information: Sides of a triangle are equal to $10,9,8$

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

Sides of a triangle are equal to $10,9,8$ .

Here,

  $\begin{array}{l}10+9=19>8\\ 10+8=18>9\\ 9+8=17>10\end{array}$

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