Question

My friend has $104 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $9/yard on one side, and cheaper metal fencing which costs $4/yard for the other three sides.

What are the dimensions of the garden with the largest area she can enclose?

Answer 1

thats kind of a tricky one

Answer 2

i agree. do you have any idea how to start it?

Answer 3

hmmm I would just start drawing pictures and start making some calculations

Answer 4

i have 9y+4y+8x=104 i am just not sure like what to plug it into to turn it into a quadratic

Answer 5

whats 8x?

Answer 6

the two metal sides. since it is a rectangle i thought that. y=length, while x=width

Answer 7

sorry, should be 13y + 8x = 104

Answer 8

so yes, you were correct.

Answer 9

How would i find the max peremiter or area. plugged it into xy=a but that is at the origin.

Answer 10

0=-1.625y^2+13y

Answer 11

The largest area will be a square.

Answer 12

the problem asks for a rectangle however, will the largest area always be in a square?

Answer 13

yes

Answer 14

a square is a rectangle.

Answer 15

so just to get this straight, when a problem asks for max area, alaways find a square? and how i use the equation i solved for y to find the area or perimeter?

Answer 16

For a given perimeter, the maximum area is that of a square. For your problem: 9x+12x=104 where x is a side of the square.

Answer 17

i see, because y=x because it is a square?

Answer 18

yes

Answer 19

is 104/21 correct for a side?

Answer 20

That's what I got.

Answer 21

9x=44.57
12x=59.43 but it says this is wrong

Answer 22

actually nevermind that is the price not length

Answer 23

it actually still says that is incorrect. it says to round to 2 decimal places and iput 4.95

Answer 24

21x=104
x=4.95
Area = x^2=24.53

Answer 25

4.95 yd by 4.95 yd are the dimensions

Answer 26

i know, i just emailed my teacher because all of the math add up, thank you for your help

Answer 27

yw