In a triangle, the length of two larger sized are 24 and 22 cm respectively. If the angles are in A.P., then the length of the third side is :

let the angles be a-d,a,a+d
w.k.t, IN A TRIANGLE  SUM OF ANGLES IS 1800 
=>a-d+a+a+d=180
=>3a=180
=>a=60⁰
the length corresponding to angle a is 22cm

by cosine rule ,
COS60=​x²+576-484
               2*x*24
1/2(48x)=x²+92
24x=x²+92
​ 
X²-24X+92=0
X=12+2(13)^{1/2 [SOLVING QUADRATIC EQN]
THEREFORE,
REQRD LENGTH OF THIRD SIDE IS}  12-2(13)^1/2cm.