पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

:
(15/4)^2 - (9/4)^2 = (225 - 81)/16 = 144/16 = 9 = 3^2!
(13/4)^2 - (x)^2 = 3^2 => x^2 = 169/16 - 144/16 = 25/16 => x = 5/4!
Wait! 9/4 + 5/4 = 14/4 = 7/2!
Wait, what if base = 4? Then 5/4 + 9/4 = 14/4 = 3.5 != 4.
What if obtuse? 9/4 - 5/4 = 4/4 = 1!
Wait, what did the example have?
In Brahmagupta / Bhaskara:
Triangle with sides 13, 14, 15: area is 84.
Divide by 4: sides are 13/4, 14/4, 15/4!
Base = 14/4!
Base segments: 9/4 and 5/4!
Perpendicular = 12/4 = 3!
Area = 1/2 * (14/4) * 3 = 21/4 = 5 1/4?
Wait! What if sides are divided by