SOLUTION: This is one is tough! A rectangular enclosure is made with 100 ft. of fencing on three sides. The fourth side is the wall of a barn. Find the greatest possible area of such an

Algebra.Com
Question 174569: This is one is tough!
A rectangular enclosure is made with 100 ft. of fencing on three sides. The fourth side is the wall of a barn. Find the greatest possible area of such an enclosure. My choices are as follows: A) 400ft^2 B) 625 ft^2 C) 1111.1 ft ^2 D) 2500ft^2.
Found 2 solutions by nerdybill, Edwin McCravy:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
If you only have 100 feet of fencing, this means that the perimeter has a maximum of 100 feet.
.
Let x = width
and y = length
.
Perimeter = 2x+y
100 = 2x+y
solving for y:
y = 100 - 2x
.
Area = xy
substituting in our value of y:
Area = x(100 - 2x)
Area = -2x^2 + 100x
.
This is essentially a parabola that opens downward (from the coefficient -2). So, all we need to do is to find the vertex to find the maximum.
.
The x coordinate = -b/2a
The x coordinate = -(100)/2(-2)
The x coordinate = (-100)/(-4)
The x coordinate = (100)/(4)
The x coordinate = 25 feet (width)
.
Length is:
y = 100 - 2x
y = 100 - 2(25)
y = 100 - 50
y = 50 feet (length)
.
Area is then:
25(50) = 1250 square feet


Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Edwin's solution:
A rectangular enclosure is made with 100 ft. of fencing on three sides. The fourth side is the wall of a barn. Find the greatest possible area of such an enclosure. My choices are as follows: A) 400ft^2 B) 625 ft^2 C) 1111.1 ft ^2 D) 2500ft^2.



 

Let y = the area.



The vertex of the parabola 
is , so the vertex here is ,  

The graph is 

So the maximum area is .  That is not one of the
choices, so the problem is botched somehow.

Edwin
RELATED QUESTIONS

Can you help me solve: A rectangular pen is made with 100 m of fencing on three sides.... (answered by checkley75)
A farmer considers using one wall of the barn for one side of enclosure and 40 meters of... (answered by rosey51235)
a mpumalsnga farmer needs to buils a rectangular enclosure with 50m of fencing on one of... (answered by Boreal)
You have a 500 foot roll of fencing, which is to form three sides of a rectangular... (answered by Fombitz)
A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house... (answered by nerdybill)
A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house... (answered by nerdybill)
Can someone help me with this question please :-) Bonnie Wolansky has 100 ft of fencing... (answered by TimothyLamb)
Need help putting word problem into an equation. I have a quiz and test tomorrow and my... (answered by ikleyn)
A farmer wants to enclose a rectangular field with 180m of fencing. The side of the barn... (answered by stanbon)