In a triangle, length of 2 larger sides is 24 & 22 resp.. if angle r in AP, then 3rd side is.........................

Also give reason behind choice of sides...........

Dear Piyush, 

the angle opposite 22 is 60 degrees. Let third side be x,

from cosine law, 22²=x²+24² -2*24*x*cos(60)

x²-24x+92=0

x=12±√52=12±2√13

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Chetan Mandayam Nayakar – IIT Madras  

let ABC be the triangle...

angles are in ap so 2B=A+C...........1

                          A+C=90-B..........2

         from 1 and 2

B=60 and so A and C can be 30 and 90

 now draw a triangle ABC right angled at C

    AB is the hypotenuse therefore AB=24

let the other sides be 22 and x

 now 24^2 =22^2 +x^2

         X=+-2sqrt23

te angle opposite to 22 is 60 degrees,let the third side be a

now from cos rule 22^2=x^2+24^2-2*x*24 Cos60

                 x^2-24x+92=0

       x = 12+-rt52=12+-2rt13