Question

A 1 meter long wire is to be divided into two pieces, one in a circular shape and the
other into a square as shown in below figure, what must be the individual lengths
so that the total area is minimised?
1 meter
Circle
Square​

Answer 1

Step-by-step explanation:

length of the rope is L. Let's assume it is divided into x and (L-x)

Rope with length x is used to make circle while the other is used to make a square

f (x)=total area= pi.x^2+(L-x)^2

If u differenciate the function and put it equal to 0, you'll get

x=L/(pi+1)

To know whether it's a maxima or minima calculate the double derivative of f (x) which is 2 (pi+1)...positive value and hence this value of X will give u the minimum value of the function f (x)

Min area=(L^2). (pi/(pi+1))

Since it is a quadratic equation and it's max value depends on the max value of x which is L, hence the maximum value of f (x) is pi.(L^2)

Hope it's help you ❤❤❤

Answer 2

Answer:

0.44 m, 0.56m

circle and rectangle