A couple of questions regarding AREAS (and getting the formulas,etc.)

  • Thread starter Thread starter mathzeroh
  • Start date Start date
  • Tags Tags
    Areas Couple
Click For Summary

Homework Help Overview

The discussion revolves around optimizing the area of a garden enclosed by a fence, given a total length of 80 feet. Various configurations are considered, including a barn on one side, a garden with dividers, and an L-shaped barn. Participants are exploring how to derive the area formulas for these setups.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to formulate the area equations for different garden designs and are questioning the correctness of their expressions. There is discussion about using the quadratic formula and finding the vertex of the area functions.

Discussion Status

There is ongoing dialogue about the validity of the area equations derived by participants. Some have provided guidance on correcting the equations, while others express confusion about the implications of their calculations. Multiple interpretations of the area functions are being explored.

Contextual Notes

Participants are grappling with the implications of their equations and the potential for different variable definitions affecting their results. There is a noted concern about typos and misunderstandings in the mathematical expressions presented.

  • #31
Yes,it's correct.

Daniel.
 
Physics news on Phys.org
  • #32
dextercioby said:
Yes,it's correct.

Daniel.

who? me? :rolleyes:
 
  • #33
Wasn't the length of the fence supposed to be 80 feet? I think you used 40...
 
  • #34
mathzeroh said:
who? me? :rolleyes:


Yes,u are correct...Does it sound unbelievebly well,or what...? :-p

Daniel.
 
  • #35
Sorry, I made a mistake... You were right.
 
  • #36
dextercioby said:
Yes,u are correct...Does it sound unbelievebly well,or what...? :-p

Daniel.

:bugeye: yes! that is unbelievable.

christinono ur just trying to scare me. :-p


im going to work on number four now. :wink:

so, so far these are the answers:

1. Area = 800 sq. ft.

2. Area = 533.3333333... sq. ft.

3. Area = 200 sq. ft.

and now four...
 
  • #37
did it work? :wink: (just kidding...)
 
  • #38
I did question 2 and got the same answer. Is that unbelievable too? :smile:
 
  • #39
For the last point (#4),i get the area
S=666.125 ft^{2}

if u don't include the rectangle of sides 7 and 36.5.

If u do,then the total area is 921.625 ft^{2}

Daniel.
 
  • #40
dextercioby said:
For the last point (#4),i get the area
S=666.125 ft^{2}

if u don't include the rectangle of sides 7 and 36.5.

If u do,then the total area is 921.625 ft^{2}

Daniel.
Really?
I got the sides to be: 13.25ft, 20.25ft, 46.5ft
and the area to be 1091.125 sq. ft.

But maybe I'm wrong...
 
  • #41
Hahahaha, yes it did, and yes, that is amazing still! :-p


OK, here's what i got for the last one:

width=y
length=x


Width = 23.25
Length = 46.5

Area = 1081.125

IS THAT AMAZING, TOO? please tell me it is or I am going to jump off the Golden Gate Bridge right now! :biggrin:
 
  • #42
uh oh, looks like we've got three different answers here...hmm...what happened? i blew it somewhere maybe, but i have a feeling i was right. :confused:
 
  • #43
Yes, it is ABSOLUTELY INCREDIBLY AMAZING! :biggrin: :approve: :smile:
 
  • #44
k now I don't know if we've got the right answer... I though we did. :confused:
 
  • #45
christinono said:
Really?
I got the sides to be: 13.25ft, 20.25ft, 46.5ft
and the area to be 1091.125 sq. ft.

But maybe I'm wrong...
Sorry, typed my answer for the area wrong. I got 1081.125 sq. ft. too!
 
  • #46
What's the area function for the rectangle in the right (similar to problem #1).Isn't it
S(x)=x(73-2x)

Daniel.
 
  • #47
dextercioby said:
What's the area function for the rectangle in the right (similar to problem #1).Isn't it
S(x)=x(73-2x)

Daniel.
The length is: 80 = (x-10) + (x-3) + y
y is: y = 80-(2x-13)
The area is: A = (x)(93-2x)
The x value of the vertex is 23.25

That's how i did it...
 
  • #48
dextercioby said:
What's the area function for the rectangle in the right (similar to problem #1).Isn't it
S(x)=x(73-2x)

Daniel.

hmm..i got this:

x=93-2y

so the area function that i got out of that was this:

A=y(93-2y)

:rolleyes: :rolleyes:
 
  • #49
mathzeroh said:
hmm..i got this:

x=93-2y

so the area function that i got out of that was this:

A=y(93-2y)

:rolleyes: :rolleyes:
Same thing I did! :smile: (just different variables)
 
  • #50
christinono said:
The length is: 80 = (x-10) + (x-3) + y
y is: y = 80-(2x-13)
The area is: A = (x)(93-2x)
The x value of the vertex is 23.25

That's how i did it...

pretty similar to how i did it except my variables in the equations that i worked with are switched from what u used. but hey, a rose by any other name is just as sweet eh? i mean a variable is a variable. :-p
 
  • #51
christinono said:
Same thing I did! :smile: (just different variables)

exactly. :smile:
 
  • #52
Okay guys the total LENGTH OF THE WIRE/FENCE NEEDS TO BE 80,REMEMBER? :rolleyes:

Take the rectangle from the right (similar with the one in the first problem).The total legth available is 80-(10-3)=73 ft...

The area function is
S(x)=x(73-x)

which gives a maximum area of 666.125ft squared.

If u add the rectangle which has fence only on one out of the 4 sides,the total area becomes 921.625.

Daniel.
 
  • #53
NOTE:There's no fence along the 10 feet side,simply because the bolded line/contiur does not include that portion...

Daniel.
 
  • #54
true. But this is what i did:

there were three 3 sides to be dealt with:

y-3
y-10
x

these. (and maybe christinono used the same thing except switched the variables).

so this is what i did, i put the ys together:

y-3+y-10

put the like terms together:

2y-13

and that's how i went forward with it...is that right?
 
  • #55
dextercioby said:
Okay guys the total LENGTH OF THE WIRE/FENCE NEEDS TO BE 80,REMEMBER? :rolleyes:

Take the rectangle from the right (similar with the one in the first problem).The total legth available is 80-(10-3)=73 ft...

The area function is
S(x)=x(73-x)

which gives a maximum area of 666.125ft squared.

If u add the rectangle which has fence only on one out of the 4 sides,the total area becomes 921.625.

Daniel.
Daniel, I don't agree. We are looking for the area of the WHOLE garden, not just the area enclosed by the fence. When I said that:
80 = (x-10) + (x-3) + y, I was saying the total length of the fence was 80 ft. What was represented by "x" was the total bottom side (same as the top), not just the length of the wire on the bottom.
 
  • #56
No.You should add:
10-3+y+2x=80

And the total area is y(x+7).

Daniel.
 
  • #57
dextercioby said:
No.You should add:
10-3+y+2x=80

And the total area is y(x+7).

Daniel.
I don't understand what you mean or what is wrong with how we solved the problem. :confused:
 
  • #58
Daniel, could you define what "x" is in your equation?
 
  • #59
christinono said:
Daniel, I don't agree. We are looking for the area of the WHOLE garden, not just the area enclosed by the fence.


The fence does not inclose an area,because it's not an enclosed curve... :wink:



christinono said:
80 = (x-10) + (x-3) + y, I was saying the total length of the fence was 80 ft. What was represented by "x" was the total bottom side (same as the top), not just the length of the wire on the bottom.


Yes,we're not talking about the same area...

This problem is confusing...

Daniel.
 
  • #60
christinono said:
Daniel, could you define what "x" is in your equation?

"x" is the length of the part of the fence which is left "outside" to form the exterior rectangle...

Daniel.
 

Similar threads

Construction Short Dividing fence on my property: what are my options?
  • · Replies 16 ·
Replies
16
Views
3K
MHB Garden Materials Help: Calculate Circumference, Perimeter, Areas & Costs
  • · Replies 1 ·
Replies
1
Views
2K
What Is the Maximum Area a Farmer Can Fence Using Different Lengths of Material?
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Can a Farmer Minimize the Cost of Fencing a Rectangular Field?
  • · Replies 2 ·
Replies
2
Views
4K
What Are the Dimensions to Minimize Fence Length for a 384 ft² Study Area?
  • · Replies 2 ·
Replies
2
Views
2K
Maximizing area word problem WITHOUT LP formula
  • · Replies 1 ·
Replies
1
Views
2K
How to Verify Maximum Area of a Rectangular Pen with Limited Fencing?
  • · Replies 1 ·
Replies
1
Views
3K
Really with word problem - maximizing area
  • · Replies 1 ·
Replies
1
Views
2K
MHB Flowerchild1993's question at Yahoo Answers regarding minimizing cost of fence
  • · Replies 1 ·
Replies
1
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K