Problema Solution
An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen by enclosing the corner of the room with two fences. If the woman has 10 feet of fencing material, what is the maximum area the playpen could encompass?
Answer provided by our tutors
Let 'x' and 'y' represent the dimensions of the rectangular playpen.
x + y = 10
y = 10 - x
The area of the rectangular playpen is:
A = x*y
Plug y = 10 - x into the above equation:
A = x(10 - x)
A = - x^2 + 10x
We need to find the maximum of the parabolic function A = -x^2 + 10x
A max = c - b^2/4a, where a = -1, b = 10, c = 0
A max = 0 - 10^2/(4*(-1))
A max = 25 ft^2
The maximum area the playpen could encompass is 25 feet square.