Question

Two sides of a ∆ have lengths 28cm and 82 cm. The measure of the third side is a whole number of centimeters. • What is the longest the third side can be? • What is the shortest the third side can be?

Answer 1

You need to remember the Triangl inequality Theorem. This states that

Let be "a", "b" and "c" the sides of a triangle. According to the Theorem mentioned above:

`\begin{gathered} a+b>c \\ b+c>a \\ a+c>b \end{gathered}`

In this case, knowing two sides of the triangle, you can set up that:

Let be "c" the third side of this triangle. You know that:

Therefore, as you can notice, the third side can be less than 110 centimeters.

Based on the explained before, you can conclude that the third side can be:

And it can be:

The answers are:

- The longest the third side can be is:

- The shortest the third side can be is: