Can we further generalise the conjecture? Class 8

Can we further generalise the conjecture? Class 8

Question 1.

Can we further generalise the conjecture? Class 8

Solution:

Yes.

Question 2.

Is (5, 12, 13) a primitive Baudhayana triple? What are the other primitive Baudhayana triples with numbers less than or equal to 20? Class 8

Solution:

Yes. Other primitive Baudhayana triple with numbers less than 20 is (8, 15, 17).

Question 3.

Generate 5 scaled versions of each of these primitive triples. Are these scaled versions primitive? Class 8

Solution:

With (3,4,5), required 5 scale versions are (6, 8, 10), (9, 12, 25), (12, 16, 20), (15, 20, 25), and (18, 24, 30).

With (5, 12, 13), required 5 scale vrsions (10, 24, 26), (15, 36, 39), (20, 48, 52), (25, 60, 65) and (30, 72, 78).

With (8, 15, 17), the required 5 scale versions are (16, 30, 34), (24, 45, 51), (32, 60, 68), (40, 75, 85) and (48, 90, 102).

With (7, 24, 25), the required 5 scale versions are (14, 48, 50), (21, 72, 75), (28, 96, 100), (35, 120, 125) and (42, 144, 150),

With (12, 35, 37), the required 5 scale versions are (24, 70, 74), (36, 105, 111), (48, 140, 148), (60, 175, 185) and (72, 210, 222).