find the Pythagorean triplet using the given number 13
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smallest side a = 13
The other side = b , if a is odd b has to be even
& hypotenuse = h
So, a² + b² = h²
=> 13² = h² - b²
=> 169 = ( h+b) ( h - b)
=> 169 = 169 x 1 ( if a is odd, we take h- b = 1 & if a is even , we take h - b = 2
Here, for a = 13, h - b = 1 ,
So, h & b are consecutive numbers…
But h + b = 169 , So 2 consecutive numbers the sum of which = 169, can be found out by dividing (169–1) by 2. So, those consecutive numbers are 84 & 85. As a is odd , so b has to be even . So, we do (169–1)/2
So, tiplet is, a = 13, b= 84 & h = 85 ……….. ANS
& 85² = 13² + 84²
=> 7225 = 169 + 7056 ( verified)
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