Exercise 13 Page 514

We are given the set of three numbers, and want to determine whether they form a Pythagorean triple. Therefore, we have to check if a triangle with the given lengths of sides is 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 substitute a=32, b=60, and c=68 into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

32^2+ 60^2? = 68^2

CalcPow

Calculate power

1024+3600 ? =4624

AddTerms

Add terms

4624=4624

The values produce a true statement, so the described triangle is a right triangle and, as a result, the given set of numbers form a Pythagorean triple.