algebra
posted by Megan
OLD MCDONALD IS GOING TO PUT A PIG PEN UP AGAINST HIS BARN. HE HAS 45 FEET OF FENCING AND WILL ONLY NEED TO MAKE 3 ADDITIONAL SIDES, AS THE BARN ACTS AS THE FOURTH SIDE.. WHAT IS THE MAXIMUM AREA THAT THE PIG PEN CAN HAVE.

Scott
area = x * y
x + 2y = 45 ... x = 45  2y
substituting ... a = 45 y  2 y^2
ymax = b / 2a = 45 / (2 * 2) = 11.25
x = 22.5
a = 22.5 * 11.25 = 253.125 
Reiny
or,
by Calculus
short side  x
single long side  y
2x + y = 45
y = 452x
Area = A = xy = x(452x)
= 45x  2x^2
dA/dx = 45  4x = 0 for a max of A
4x = 45
x = 45/4 , then y = 452(45/4) = 45/2
max area = xy = (45/4)(45/2)
= 2025/8
= appr 253.125 , same as Scott
Respond to this Question
Similar Questions

math
a rectangular pen is to be constructed alongside a barn using 120 feet of fencing. the barn will be used for one side of the pen. What should the dimensions of the pen be to maximize its area. ***Can not use calculus. This is a 9th … 
algebra
Ian wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Ian has 450 feet of fencing, what dimensions would maximize the area of … 
Math, Quadratics
Farmer John is building a pen to keep his pig in. John has 40m of fencing. He will only need to make 3 sides to the pen because the 4th side will be along a barn. If John wants the maximum area what should the side lengths of the pen … 
math
Farmer Hodges has 50 feet of fencing to make a rectangular hog pen beside a very large barn. He needs to fence only three sides because the barn will form the fourth side. Studies have shown that under those conditions the side parallel … 
calculus optimization problem
A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the pen … 
math
a rectangular garden with an area of 2112 square feet is to be located next to a barn with fencing on three sides and the barn acting as the fourth side.Write a function that gives the length of fencing needed if the length of the … 
precalc
Old McDonald has 1000 feet of fencing, and wants to build a pen along the side of his barn that will have two separate areas one for his pigs, and one for his cows. if only one of the fences is to run parallel to the barn, find the … 
Math
Farmer wants to enclose a rectangular area that is 600 sq. ft. He is using his barn for one of the sides. The barn is 30 feet long and he does not want the pen to extend longer than the barn. How much fencing will need to be purchased? 
Algebra
A rectangular pig pen is made of 84 meters of fencing on three sides. The fourth side is a barn wall. Find the dimensions and greatest possible area of the enclosure. 
algebra
A farmer has 25 yards of fencing to make a pig pen. He is going to use the side of the barn as one of the sides of the fence, so he only needs to fence 3 sides. What should be the dimensions of the fence in order to maximize the area?