Question 1189288
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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  {{{(1/2)*a*b)}}} = {{{(1/2)*4*3}}} = 2*3 = 6 square units.    


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


    c = {{{sqrt(3^2 + 4^2)}}} = {{{sqrt(9 + 16)}}} = {{{sqrt(25)}}} = 5 units long.    <U>ANSWER</U>
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Solved and explained.