Find 5 more Baudhayana triples using this idea. Class 8

Find 5 more Baudhayana triples using this idea. Class 8

Question 1.

Find 5 more Baudhayana triples using this idea. Class 8

Solution:

49 is an odd square number. It is the 25th odd number (49 = 2 × 25 - 1).

So, 1 + 3 + 5 + ... + 49 = 25².

We have n = 5.

So, (25 - 1)² + 49 = 25².

or 24² + 7² = 25².

So, (7, 24, 25) is a Baudhayana triples.

81 is an odd square number. It is the [latex]\frac{81+1}{2}[/latex] = 41th odd number.

So, (41 - 1)² + 81 = 41², i.e., 40² + 9² = 41².

So, (9, 40, 41) is another Baudhayana triple.

Similarly, with odd square number 121, we get (61 - 1)² + 121 = 61².

So, 60² + 11² = 61².

So, another triple is (11, 60, 61).

With odd square number 169, we get

(85 - 1)² + 169 = 85², i.e., 84² + 13² = 85².

Hence, another triple is (13, 84, 85).

Finally, with odd square number 225,

(113 - 1)² + 225 = 113².

So, 112² + 15² = 113².

Hence, fifth triple is (15, 112, 113).

Question 2.

Does this method yield non-primitive Baudhayana triples? Class 8

[Hint : Observe that among the triples generated, one of the smaller sidelengths is one less than the hypotenuse.]

Solution:

Yes.