Answer:
Wire should be cut in two parts with the length = 15.69 ft and 12.31 ft
Step-by-step explanation:
Length of the wire = 28 ft has been cut in two pieces.
One piece is used to form a square and remaining piece to form a circle.
Let the length of the wire which forms the square is 'l' ft.
Area of the square = (side)²
Perimeter of the square = 4(side) = l
Length of one side =
So, the area of the square = ft²
Now length of the remaining part = perimeter of the circle = (28 - l) ft
2πr = (28 - l)
r =
Area of the circle formed = πr²
=
=
Combined area of the square and circle
= +
= +
Now to maximize the area we will find the derivative of the area with respect to l.
=
=
Now equate the derivative to zero.
= 0
l(4 + π) = 112
l(4 + 3.14) = 112
l =
l = 15.69 ft
Length of the other part = 28 - 15.69 = 12.31 ft
Therefore, wire should be cut in two parts with the length = 15.69 ft and 12.31 ft
