Question

1, 3, 4, and 5 are the basic Pythagorean Triple because 3 squared + 4 squared = 5 squared. Which of the following is the same triple scaled up by 6?

a) 36, 46, 56
b) 18, 24, 30
c) 9, 10, 11
d) 7, 24, 25

Answer 1

The Pythagorean triple scaled up by a factor of 6 from the basic 3, 4, 5 triple is 18, 24, 30, which satisfies the Pythagorean relationship a² + b² = c².

Step-by-step explanation:

The question is about the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. To scale up a Pythagorean triple by a factor, each number in the triple is multiplied by that factor. In this case, the basic Pythagorean triple is 3, 4, 5, and it is scaled up by 6. Therefore, we multiply each term by 6 to get the new triple: 18, 24, 30.

The scaled up triple must still satisfy the relationship a² + b² = c². If we multiply all terms of the basic 3, 4, 5 triple by 6, we get:

• 3 * 6 = 18
• 4 * 6 = 24
• 5 * 6 = 30

Checking the relation:

18² + 24² = 30²
324 + 576 = 900
900 = 900

This confirms that option b) 18, 24, 30 is the correct answer.