Exercise 11 Page 661

Let's begin with recalling the definition of a Pythagorean Triple. A Pythagorean Triple is a set of three nonzero whole numbers a , b and c such as a^2+ b^2= c^2.Therefore, to check which of the given sets of numbers is not a Pythagorean Triple, we will check if they satisfy the above equation. Let's start with 9, 12 and 15.

9^2+ 12^2? = 15^2

CalcPow

Calculate power

81+144? =225

AddTerms

Add terms

225=225

Since we ended with a true statement, the first set of numbers is a Pythagorean Triple. We will check the rest of the sets in the same way.

Set of numbers	a^2+b^2=c^2	Simplify	Is it a Pythagorean Triple?
9, 12 and 15	9^2+ 12^2? = 15^2	225=225	Yes ✓
21, 72 and 75	21^2+ 72^2? = 75^2	5625=5625	Yes ✓
15, 36 and 39	15^2+ 36^2? = 39^2	1521=1521	Yes ✓
8, 13 and 15	8^2+ 13^2? = 15^2	223≠225	No *

As we can see, the last set 8, 13, and 15, is not a Pythagorean Triple. This corresponds with answer D.