Finding third value of Pythagoras H ² = P² + B²

Finding third value of Pythagoras H ² = P² + B² 

If we use a, b, c for sites is smallest biggest, where the biggest side she is hypotenuse or Karna in Hindi 

Finding 
a = √(c – b) (c + b )
Finding 
b = √(c – a) (c + a )
Finding 
c = (a + b) –2 × (b – W×a )
W = ? 
W is only whole number after dividing b ÷ a. In other words b ÷ a  (Leave Reminder)


Example : 1. 
3, 4, 5
Find a
a = √(5 – 4) (5 + 4 ) = √ (1)(9) = √9 = 3
Find b
B = √(5 – 3) (5 + 3 ) = √ (2)(8) = √16 = 4
Find c
W = 4÷3 =1
c = (a + b) –2 × (b – W×a )
c = (3 + 4) – 2 × (4 – 1× 3 ) = 7 – 2 (4–3) 
= 7 – 2 (1) 
= 7 – 2 
= 5


Example : 2. 
6, 8, 10
Find a
a = √(10 – 8) (10 + 8 ) = √ (2)(18) = √36 = 6
Find b
b = √(10 – 6) (10 + 6 ) = √ (4)(16) = √68 = 8
Find c
W = 8 ÷ 6 = 1
c = (a + b) –2 × (b – W×a )
c = (6 + 8) – 2 × (8 – 1× 6 ) = 14 – 2 (8–6) 
= 14 – 2 (2) 
= 14 – 4
= 10

Example : 3
9, 12, 15
Find a
a = √(15 – 12) (15 + 12 ) = √ (3)(27) = √81 = 9
Find b
b = √(15 – 9) (15 + 9 ) = √ (6)(24) = √144 = 1w
Find c
W = 12 ÷ 9 = 1
c = (a + b) –2 × (b – W×a )
c = (9 + 12) – 2 × (12 – 1× 9 ) = 21 – 2 (12–9) 
= 21 – 2 (3) 
= 21 – 6
= 15

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