question_answer 85)

A wire of length 28m is to be cutr into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum? 

Answer:

Let AB = 28 m be the length of the wire.         AC = x m, and CB = (28 ? x) m be the two pieces of the wire.       Let the piece AC is to be made into square of side a meters and CB into a circle of radius r meters.        Perimeter of the square = x        4a = x             and circumference of the circle = 28 ? x                                      Combined area of the square and the circle                    A = a2 +                                                       Now              is minimum when                                     Hence the combined area will be minimum if length of the pieces are  metres and metres.