Pythagorean Triples and Systems of Equations

This lesson explores Pythagorean triples, starting with the basic 3, 4, 5 triple and explaining how to scale it to find new triples. It also covers using known triples like 5, 12, 13 to identify new ones. The lesson distinguishes between Pythagorean triples and other triples, emphasizing the need for integer values. An extension problem introduces the historical Plimpton 322, a stone tablet listing Pythagorean triples. The lesson concludes with a method to find triples using systems of equations.

What is a Pythagorean triple?

• A set of three numbers that are all odd

• A set of three numbers that are all even

• A set of three numbers that satisfy a^2 + b^2 = c^2

• A set of three numbers that are all prime

If you multiply the Pythagorean triple 3, 4, 5 by 3, what new triple do you get?

• 12, 16, 20

• 6, 8, 10

• 9, 12, 15

• 15, 20, 25

Which of the following is a Pythagorean triple derived from 5, 12, 13?

• 25, 60, 65

• 15, 36, 39

• 10, 24, 26

• 20, 48, 52

What distinguishes a Pythagorean triple from a non-integer triple?

• Pythagorean triples must be integers

• Non-integer triples are always larger

• Pythagorean triples are always even

• Non-integer triples are always odd

What is the significance of the Plimpton 322?

• It is a historical artifact listing Pythagorean triples

• It is a modern tool for calculating triangles

• It is a book on geometry

• It is a mathematical theorem

Where was the Plimpton 322 discovered?

• Iraq

• Greece

• India

• Egypt

In the system of equations X + Y = T/S and X - Y = S/T, what must be true about T and S?

• S must be greater than T

• T and S must be equal

• T and S must be prime

• T must be greater than S

Using the system of equations, what is the Pythagorean triple for S = 4 and T = 5?

• 5, 12, 13

• 8, 15, 17

• 7, 24, 25

• 9, 40, 41

What is the result of solving the system of equations for S = 7 and T = 10?

• 15, 36, 39

• 30, 40, 50

• 21, 28, 35

• 51, 140, 149

What is the Pythagorean triple for S = 1 and T = 4 using the system of equations?

• 9, 12, 15

• 15, 8, 17

• 3, 4, 5

• 5, 12, 13