SOLUTION: you have a 1200 foot roll of fencing and a large field. You want to make 2 paddlocks by splitting a rectangle enclosure in half. What are the dimensions of the largest such enclos

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: you have a 1200 foot roll of fencing and a large field. You want to make 2 paddlocks by splitting a rectangle enclosure in half. What are the dimensions of the largest such enclos      Log On


   



Question 172502: you have a 1200 foot roll of fencing and a large field. You want to make 2 paddlocks by splitting a rectangle enclosure in half. What are the dimensions of the largest such enclosure
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let width = w
Let length = l
Let area = A
3w+%2B+2l+=+1200
2l+=+1200+-+3w
l+=+%281200+-+3w%29%2F2
A+=+w%2Al
A+=+w%2A%281200+-+3w%29+%2F+2
A+=+600w+-+%283%2F2%29%2Aw%5E2
If I set A=0 to find the roots, the
maximum will be at w%5Bmax%5D+=+-b%2F%282a%29 which
is exactly 1/2 way between the roots
-%283%2F2%29%2Aw%5E2+%2B+600w+=+0
-b+=+-600
2a+=+-3
-b%2F%282a%29+=+-600%2F-3
-600%2F-3+=+200
w+=+200
And, since
3w+%2B+2l+=+1200
3%2A200+%2B+2l+=+1200
2l+=+600
l+=+300
The dimensions of the largest enclosure will
be when width = 200 ft and length = 300 ft
check answer:
3w+%2B+2l+=+1200
3%2A200+%2B+2%2A300+=+1200
600+%2B+600+=+1200
1200+=+1200
and
A+=+w%2Al
A+=+200%2A300
A+=+60000 ft2
To see if this is max area change w and l
slightly but still make 3w+%2B+2l+=+1200 true, like
w+=+200.1
l+=+299.85
A+=+299.85%2A200.1
A+=+59999.985
It ends up being a little less as it should