Exercise 6 Page 518

We have been given the segment lengths of a triangle. We will investigate whether these segment lengths form a triangle. Then, we will determine whether the triangle is acute, right, or obtuse. Let's start!

Step I

In this step, we will use the Triangle Inequality Theorem to verify that the segment lengths form a triangle. However, we first need to have approximate value of $3\sqrt{55}$ to be able to compare segment lengths.To do so, let's estimate them by looking at nearby perfect squares.