math
posted by craig .
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 grade question

If the sides have length a and b, then, assuming b is the side parallel to the barn,
a+a+b = 120, so b = 1202a
Area = a*b = a*(1202a) = 120a  2a² = 2a(60a)
Now, this is a parabola opening downward. The vertex (a maximum) is halfway between the roots, 0 and 60, at a=30
So, pen is 30x60 feet.
Respond to this Question
Similar Questions

Math
A rectangular dog pen is to be constructed using a barn wall as one side and 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area. 
math
a farmer has enough fencing to build 40 feet of fence. He wishes to build a rectangular pen nest to his barn wall forming one side of the pen. What dimension should he make the pen so as to enclose the greatest possibility area? 
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 … 
Geometry
A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen? 
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 … 
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
Manuel 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 Manuel has 750 feet of fencing, what dimensions would maximize the … 
math
Trent 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 Trent has 400 feet of fencing, what dimensions would maximize the area … 
Help please? Math 141 (PreCal) (Shapes)
Hi everyone I am lost on how to do this math problem: A. You have 180 feet of fencing with which to construct a rectangular pen. What is the maximum area you can enclose? 
math
a. A rectangular pen is built with one side against a barn. 1200 m of fencing are used for the other three sides of the pen. What dimensions maximize the area of theâ€‹ pen?