A set of 3 whole numbers that satisfy the equation a2 + b2 = c2 This is the most basic, and most common Pythagorean Triple and is often called a 3-4-5 Right Triangle.

7 24 49 576 625 25 a2 + b2 = c2 92 + 122 = x2 81 + 144 = x2 225 = x2 15 = x

6 5 36 25 11 25 √11 3.317 3.317

a2 + b2 = c2 x2 + 3.52 = 52 x2 + 12.25 = 25 x2 = 12.75 x = √12.75 x ≈ 3.571ft 3.5ft 5ft x

height right 17 8 289 64 225 64 15 16 15 120 120

Here's a way to generate the triples: Let n and m be integers where n>m. Then, define a = n2 - m2, b = 2nm, c = n2 + m2 Substitution gives: (n2 - m2)2 + (2nm)2 = (n2 + m2)2 If n = 4 and m = 2, the rule would produce the Pythagorean Triple 12, 16, 20.

17 3 3 3 17 3 51 576 2025 2601 51

a2 + b2 = c2 142 + h2 = 502 196 + h2 = 2500 h2 = 2304 h = 48 A = 1/2bh A = 1/2(28)(48) A = 672ft2 h This is a multiple of the 3, 4, 5 triangle, so x = 50.