Exercise 10 Page 413

We are given the lengths of the three sides of a triangle, and want to determine whether the sides form a right triangle. We will need to use the Converse of the Pythagorean Theorem.

Converse of the Pythagorean Theorem

If the sides of a triangle have lengths a, b, and c, and c^2=a^2+b^2, then the triangle is a right triangle.

This tells us that we can use the Pythagorean Theorem in reverse to test if a triangle is right. In general, the hypotenuse c has the greatest value. Let's look at the given triangle.

Let's substitute a=8.5feet, b=8feet, and c=11.5feet into a^2+b^2=c^2, and see if they produce a true statement. The values produce a false statement, so the described triangle is not a right triangle.