Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct? Can a Pythagorean triple be created using multiples of a known Pythagorean triple.
Answer
A
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
B
Yes, as long as each number in the Pythagorean triple is multiplied by a different whole number.
C
No, Pythagorean triples only exist with small numbers.
D
No, multiplying a known Pythagorean triple by a whole number will not create a Pythagorean triple.
Explanation
Yes. Multiplying each number in a Pythagorean triple by the same whole number preserves the relationship: if a² + b² = c², then (ka)² + (kb)² = (kc)². Here, 24² + 32² = 576 + 1,024 = 1,600, and 40² = 1,600. So Tess’s triple works, and the correct choice is “Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.”
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