Question

Shakira plans to build a 4 side-by-side rectangular enclosure whenever/wherever she wants around her garden. SHE DECIDES TO USE HER HOUSE AS ONE SIDE OF THE GARDEN. She has 1800 ft of fence. What would be the length and width of the garden for maximum AREA? What is the max area?

Answer 1

calc or no? doesn't make a difference, just asking

Answer 2

yep. calculus :)

Answer 3

draw it, and total the perimeter using a variable for length and width

Answer 4

not needed but we can do it that way

Answer 5

first off, although i am not supposed to give a direct answer, lets answer it first

Answer 6

use half of the fence for the side opposite the house, split the remaining half for the other two sides
there, i said it, now lets find it

Answer 7

right

Answer 8

how much is left for the part of the fence not labelled?

Answer 9

A=lw so A=(1800-2x)(x) ??

Answer 10

bingo

Answer 11

now for the lets not use calculus part, because it is unnecessary \[A(x)=1800x-2x^2\] is a parabola that opens down
the max is at the vertex use \(-\frac{b}{2a}\) to find it

Answer 12

i thought the thing was 4 rectangles side by side p=5x+y,, maybe not

Answer 13

or if you are a slave to calc, take the derivative, set it equal to zero and solve
you will still get \(-\frac{b}{2a}\)

Answer 14

oh crap i should learn how to read !!!

Answer 15

ignore all i said, @DanJS pointed out the correct question

Answer 16

not sure, you may be right, enclosure is singular, not 4 of em..

Answer 17

x-450

Answer 18

sorry, x=450

Answer 19

either way, same process to solve , sorry

Answer 20

i am not sure what a "4 side by side" rectangular enclosure is
maybe it is this

Answer 21

no i am sorry, i didn't read carefully enough

Answer 22

right. that's what i was thinking

Answer 23

then it is \(A=x(1800-5x)\) and the solution is different

Answer 24

so x is not 450?

Answer 25

not any more

Answer 26

now \[A=1800x-5x^2\] so it is different

Answer 27

i mean the work is the same, but the answer is different

Answer 28

ok, one moment while i try to solve for x

Answer 29

ok, take the derivative first of course, then set that equal to zero

Answer 30

take the derivative of 1800x-5x^2?

Answer 31

yes

Answer 32

A(x)= 1800x - 5x^2 --> 1st D= 1800-10x

Answer 33

x= 180

Answer 34

yes

Answer 35

so now, A=(180)(w)

Answer 36

\[
A=180(1800-5\times 180)\]

Answer 37

ah, so plug in 180 for x into x(1800-5x)

Answer 38

yes

Answer 39

-1296000?

Answer 40

no

Answer 41

http://www.wolframalpha.com/input/?i=180%281800-5*180%29

Answer 42

oh, i see what i did wrong. it's 162000

Answer 43

looks good

Answer 44

dimensions are 180 x 900

Answer 45

yes i think so

Answer 46

THANK you so much! this really helped me. :)

Answer 47

yw