Problema Solution
a rectangular playground is to fenced off and divided into two by another fence parallel to one side of the playground. Four hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area what is the maximum area
Answer provided by our tutors
Let 'x' and 'y' represent the length of the sides of the playground, and 'x' the length of the fence parallel to one side
3x + 2y = 400
y = 200 - (3/2)x
The area of the playground is:
A = x*y
plug y = 200 - (3/2)x into the last equation:
A = x*(200 - (3/2)x)
A = -(3/2)x^2 + 200x
We need to find such x for which A has maximum:
x = -b/(2a), where a = -3/2 and b = 200
x = -200/(2*(-3/2))
x = 66.67 ft
y = 200 - (3/2)*(-200/(2*(-3/2)))
y = 100 ft
The dimensions of the playground are: 66.67 ft and 100 ft.