let p,q and r be the sides of the triangle PQR.
then according the properties of triangle
p/sinP = q/sinQ = r/sinR = k. So
p = k*sinP, q = k*sinQ and r = k*sinR. and 2q = p + r
Let L1, L2 and L3 be the altitudes from P. Q and R points,
then the area of the triangle PQR is given by
1/2*p*L1 = 1/2*q*L2 = 1/2*r*L3 = A
So p = 2A/L1, q = 2A/L2 and r = 2A/L3.
Now can you proceed?