Chapter 6.4, Problem 8CE

To determine

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

Answer to Problem 8CE

No, it is not possible to have a triangle with sides equal to $6,6,20$

Explanation of Solution

Given information: Sides of a triangle are equal to $6,6,20$

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 $6,6,20$ .

Sum of two sides $=6+6=12$

Third side $=20$

  $12<20$

So,

As addition of any two sides of a triangle is not greater than the remaining side, it is not possible to have a triangle with such sides.