The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c5.s3.10

c5.s3.10

a) n²+(¾n)² = (5/4n)² (*Bśl.* 1.5; *Mśl.* 1.11—1.12)
(i) n = 4, 4²+3² = 5² (*Bśl.* 1.13)
(ii) n = 12, 12²+9² = 15² (*Kśl.* 2.5)
(iii) n = 20, 20²+15² = 25² (*Āśl.* 5.3)
(iv) n = 16, 16²+12² = 20² (*Āśl.* 5.3)
b) n²+(5/12n)² = (13/12n)² (*Bśl.* 1.8; *Āśl.* 1.2; *Kśl.* 1.4)
(i) n = 1, 1²+(5/12)² = (13/12)² (*Bśl.* 1.8 *Āśl.* 1.2; *Kśl* 1.4-1.5)
(ii) n = 36, 36²+15² = 39² (*Bśl.* 1.13; *Āśl.* 5.4)
(iii) n = 188, 188²+(78⅓)² = (203⅔)² (*Āśl.* 6.5)
(iv) n = 6, 6²+(2½)² = (6½)² (*Āśl.* 6.6; *Mśl.* 2.4)