If (a, b ) and (c ) are the sides of ( A B C ) for which (r₁=8, r₂=12 ) and (r₃=24 ), then the ordered triad ((a, b, c)= )

Step-by-step solution

It is given that ( aligned r₁ & =8= s-a (i) & r₂=12= s-b (ii) and r₃ & =24= s-c (iii) aligned ) From Eqs. (i) and (ii), we get ( gathered s-b s-a = 2 3 3 s-3 b=2 s-2 a 5 a+c=5 b (iv) gathered ) From Eqs. (ii) and (iii), we get ( array cc & s-c s-b = 1 2 & 2 s-2 c=s-b & a+3 b=3 c (v) array ) and from Eqs. (i) and (iii), we get ( array cc & s-c s-a = 1 3 & 3 s-3 c=s-a & 2 a+b=2 c (vi) array ) On solving Eqs. (iv), (v) and (vi), we get ((a, b, c)=(12,16,20) ) Hence, option (2) is correct.