Question

Two sides of a triangle have lengths $7$ and $9$. Which of the following could not be the length of the third side?

• A. $4$
• B. $5$
• C. $7$
• D. $11$
• E. $16$

Answer 1

The correct option is E $16$

An important rule to remember about triangles is called the third side rule:

The length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the (positive) difference of the lengths of the other two sides.

For this triangle, the length of the third side must be greater than $9-7=2$97=2 and less than $9+7=16$9+7=16. All the answers are possible except for answer E, which is equal to $16$16 but not less than $16$16.