Exercise 13 Page 495

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=4, b=5, and c=6 into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

4^2+ 5^2? = 6^2

CalcPow

Calculate power

16+25 ? =36

AddTerms

Add terms

41≠ 36

The values produce a false statement, so the described triangle is not a right triangle and, as a result, the given set of numbers is not a Pythagorean triple.