Some primitive triples are ... (3, 4, 5) (5, 12, 13) (7, 24, 25) (9, 40, 41) One interesting characteristic of these is that the sum of the last two numbers is the square of the first number.
Any multiple of these will be a Pythagorean triple.
Now consider your list. a) (10, 24, 26) = 2×(5, 12, 13) . . . IS a Pythagorean Triple b) 2×(7, 24, 25) = (14, 48, 50), so (14, 48, 49) is NOT a Pythagorean Triple c) 3×(3, 4, 5) = (9, 12, 15), so (9, 12, 16) is NOT a Pythagorean Triple d) (9, 40, 41) . . . IS a Pythagorean Triple e) 5×(3, 4, 5) = (15, 20, 25) . . . IS a Pythagorean Triple
The sets of side lengths that are Pythagorean Triples are ... (10, 24, 26) (9, 40, 41) (15, 20, 25)
14 appetizer recipes over the course of 7 weeks means she learns 2 recipes in 1 week so this means it will take her 8 weeks to learn 16 recipes. (Double check to make sure I'm correct)
