Question

A triangle has sides of length 8 cm and 3 cm. What can you say about the length of the third side? Based on the triangle theorem, I am debating between or not having any choice.B) The side is shorter than 11 cm but not necessarily longer than 5m andc) The side is shorter than 8 cm but not necessarily longer than 3 cm

Answer 1

- We know that the sum of any two sides of a triangle is always greater than the third side. So:

$\begin{gathered} third\text{ side}<8+3 \\ third\text{ side}<11 \end{gathered}$

- Also the difference of any two sides of a triangle is always less than the third side. Therefore:

$\begin{gathered} third\text{ side}>8-3 \\ third\text{ side}>5 \end{gathered}$

Combining the two equations we get:

$11>third\text{ side}>5$

This means that the third side of the triangle lies between 5cm and 11

Answer: A.