Precalc word problem. can you figure it out???

[lhammo7]

you have 6,000 feet of fencing with which to grow a garden. The enclosed area is in the shape of a rectangle, which you would then like to divide the garden into 3 equal plots (see figure) so you can have a control group in one plot and perform experiments in the other two. (it's basically one large rectangle with two fence lines going down it to make it into 3 parts)

a)what is the maximum area of land you can set aside for your rectangular garden?

b)if you can make three separate circular plots, would you have a greater or smaller total enclosed area? By approximately how many square feet?

please please help me!!! thank you so much.

what i think i figured out:

A=lw
P=4w+2l
P=6000
l=-2w+3000
A=-2w^2+3000w
maximum point: (750,1125000)
1125000=A of the rectangular garden

(please no derivatives i have not learned that yet)

part b:

P=C
C=(2(pi)r)x3
C=6(pi)r
C=6000
r=5981.15
A=(pi)r^2
A=112387823.5

the difference:112387823.5-1125000=111262823.5

that answer seems very wrong. what did i do wrong?

 

[Deleted member 4993]

you have 6,000 feet of fencing with which to grow a garden. THe enclosed area is in the shape of a rectangle, which you would then like to divide the garden into 3 equal plots (see figure) so you can have a control group in one plot and perform experiments in the other two. (it's basically one large rectangle with two fence lines going down it to make it into 3 parts)

a)what is the maximum area of land you can set aside for your rectangular garden?

Where is the figure?

Tell us whether the two dividers are also made by the given fencing material.

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

b)if you can make three separate circular plots, would you have a greater or smaller total enclosed area? By approximately how many square feet?

please please help me!!! thank you so much.

 

[lhammo7]

yes the dividers are included in the 6,000 ft. i included all my work in the original problem. i do not know how to draw the drawing in i am sorry but it is a rectangle that has 2 dividers, which turns it into 3 touching rectangles. thanks for looking into my problem.

 

[Deleted member 4993]

you have 6,000 feet of fencing with which to grow a garden. The enclosed area is in the shape of a rectangle, which you would then like to divide the garden into 3 equal plots (see figure) so you can have a control group in one plot and perform experiments in the other two. (it's basically one large rectangle with two fence lines going down it to make it into 3 parts)

a)what is the maximum area of land you can set aside for your rectangular garden?

b)if you can make three separate circular plots, would you have a greater or smaller total enclosed area? By approximately how many square feet?

please please help me!!! thank you so much.

what i think i figured out:

A=lw
P=4w+2l
P=6000
l=-2w+3000
A=-2w^2+3000w
maximum point: (750,1125000)
1125000=A of the rectangular garden

Looks good to me....

(please no derivatives i have not learned that yet)

part b:

P=C
C=(2(pi)r)x3
C=6(pi)r
C=6000
r=5981.15

\(\displaystyle r \, = \, \frac{6000}{6\cdot \pi} \, = \, 318.3098862\)

\(\displaystyle A \, = 3\cdot\pi \cdot r^2 = 954929.6586\)


A=(pi)r^2
A=112387823.5

the difference:112387823.5-1125000=111262823.5

that answer seems very wrong. what did i do wrong?

 

[lhammo7]

so then the area of the rectangle: 1,125,000 subtract the area of the three circles: 954,930.34 is 170,069.

that still looks like it is wrong. how can their be such a large difference?

what i am thinking is that to find the area of the three circles you do not need to multiply (pi)r^2 by three because it was already accounted for earlier when we did 6000=(3)2(pi)r. do we really need to add the 3 to the second problem or is it already accounted for is my question. but then i would get 318310.11 for an area and that seems even more wrong.

the two areas should be relatively similar, correct? i'm getting confused.

 

[mmm4444bot]

so then [the area of the rectangle: 1,125,000] subtract [the area of the three circles: 954,930.34] is 170,069.

that still looks like it is wrong. how can their be such a large difference?

It is more precise to write the value in your answer to part (2) as 170,070.

(Impress your instructor with a complete sentence!)

The difference is large because these are huge gardens.

With three rectangular plots, two of the sides are shared. There is no sharing with the circular plots. This "benefit" gives the rectangular arrangement the edge. Blow up the amount of fencing available, and this benefit blows up as well.

-

… do we really need to add the 3 to the second problem [?] …

Yes.

The three circles are identical, so these three radii are all equal.

When you use 6000 = 3 * 2 * Pi * r, you find this common radius.

r = 1000/Pi

When you use Pi * (1000/Pi)^2, you find the area of only one circle.

You need to multiply by three to get the aggregate area.

 

[lhammo7]

thanks so much now i get it!!