Geometry
posted by Shatina .
A horse breeder wants to construct a corral next to a horse barn that is L=16 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 280 feet of fencing available.
Find the value of x which maximizes the amount of area the corral can enclose

no figure?

Since 16 feet of fencing is not used, it is the same as if a complete rectangle of perimeter 296 were being built.
The maximum area will be for a square of side 296/4 = 74 feet.
To work it out, let x be the side with the barn in it. Then we have
2x16+2y=280
x+y=148
the area is
a = xy = x(148x) = 148xx^2
the vertex is at x = b/2a = 74
Respond to this Question
Similar Questions

grade 9 mathimathic optimizing
i am lost completly i don't know what to do. please help me!!!! a farmer is adding a rectangle corral to the side of a barn. the barn will form one side og the rectangle . the farmer has 16 m of fencing to use. conduct an investigation … 
Precalculus
The owner of a horse stable wishes to set up 4 rectangular corrals of identical dimensions along the back wall of an existing barn using 200 ft of fencing. The sides of each corral will be attached to the barn, fencing is not needed … 
Precalculus
I have a diagram that has 4 rectangular corrals joined together and a barn above it. Fencing is not needed along the back wall of the barn. The perimeter is 200 ft and the question asks... If each corral is 16 ft. long (front to back) … 
Precalculus
A barn has 150 feet of fencing and there are 3 rectangular corrals of identical dimensions along the back wall of the barn. The sides of each corral are attached to the barn and fencing is not needed along the back wall of the barn. … 
Precalculus
A barn has 150 feet of fencing and there are 3 rectangular corrals of identical dimensions along the back wall of the barn. The sides of each corral are attached to the barn and fencing is not needed along the back wall of the barn. … 
Math Please Help Us!
Diagram has 4 rectangular corrals with a barn above it. Sides (front to back) are attached to the barn. Fencing is not needed along the back of the barn. P= 200 ft of fencing If each corral is 16 ft long (front to back), how wide will … 
pre calculus
A farmer will be adding a rectangular corral to his barn. He has 600 feet of fencing. The part of the barn that is attached to the corral is 150 feet long. Write a function for the area of the corral, A(x) and include the domain Find … 
cal
a rancher has 4000 feet of fencing for constructing a rectangular corral. one side of the corral will be formed by a barn and requires no fence. three exterior fences and 2 interior fences partition the corral into 3 rectangular regions. … 
Math: pre calculus
a barn is 150 feet long and 75 feet wide. the owner has 240 ft of fencing and wants to construct two adjacent outdoor pens of identical size along the long side of the barn using the barn as one side of each pen. the owner wants the … 
COLLEGE ALGREBRA
A horse breeder wants to construct a corral next to a horse barn that is L=20 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 320 feet of fencing available.