SOLUTION: For ΔABC with three sides a, b, and c, if a=4 and b=3, then the value of c which yields max area is...

OBVIOUSLY, the triangle with two given sides  "a"  and  "b"  has the maximum area 
when the angle between these sides is the right angle.


Then the area of such a triangle is   =  = 2*3 = 6 square units.    


For such a right angled triangle, "c" is the hypotenuse


    c =  =  =  = 5 units long.    ANSWER