Question

Determine whether it is possible to draw a triangle with the given side lengths so why or why not 11,10,20

Answer 1

It is possible to draw a triangle with the given side lengths of 11, 10, and 20 because the sum of any two side lengths is greater than the length of the 3rd side as stated in the Triangle Inequality Theorem.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So given the side lengths of 11, 10, and 20, let's see if it satisfies the above conditions;

`\begin{gathered} 11+10=21\text{ and 21 > 20} \\ 11+20=31\text{ and 31 > 10} \\ 10+20=30\text{ and 30 > 11} \end{gathered}`

We can see from the above that the condition in the above theorem is satisfied, therefore, we can say that it is possible to draw a triangle with the given side lengths of 11, 10, and 20.