Draw a parallel line from the vertex to the given side.

Taking any point on this lin, if you draw a triangle with the given side, all the triangles will have the same area.

If a and b are the sides of the triangles,and b> a then angle B>A.

According to sine rule

a/sinA = b/sinB.

So a = k*sinA

b = k*sinB.

Hence a + b = k(sinA + sinB) > 2*k*sinA

So a+b will be minimum if a = b.