Question

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.544 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. Remember to reduce any fractions and simplify your answers as much as possible.
HINT: Start by drawing a picture that illustrates what is being described in the problem, then label the important parts.

Answer 1

the shorter side of the playground is _____ ft
the longer side of the playground is ____ ft
what is the maximum area?

Answer 2

give me two minutes

Answer 3

THANK YOU!!!! Finally somebody responds!

Answer 4

k wait, i did this, then i though of a better way, sorry one more minute

Answer 5

okay thanks!

Answer 6

k so, shorter side is 77.71, longer side is 155.42, and maximum area is 12,007 but if you have a minute, i'll try to get someone to check it

Answer 7

@zepdrix will you check this for me?

Answer 8

@mathstudent55 can you look at this for me?

Answer 9

@dan815 will you look at this for me?

Answer 10

those answers are incorrect

Answer 11

there are three other people viewing this, if any of them could help that'd be great

Answer 12

sorry bout that, i'm trying to get people *hint, hint*

Answer 13

Hmm I don't remember how to do maximization problems without using Calculus :O(
What class is this for? Algebra stuff?

Answer 14

yeah

Answer 15

Do you have a limited number of guesses or no?

Answer 16

Oh you logged off... awesome..

Answer 17

@zepdrix thanks for looking at this for me, i didn't think i was doing it right, but i didn't want to leave her hanging:/

Answer 18

I came up with your numbers the first time I tried it^
I was assuming both areas would have to be square to maximize it.
But I guess something else is going on.

I came up with some answers using calculus methods.
But I guess she's not around the check them :d oh well.

Answer 19

Ok, thats what i was thinking too and then I tried it where the entire area was square and there was a parallel fence cutting it into two rectangles, but that had a smaller area, so i wasn't sure:) yeah, oh well

Answer 20

haha yah i tried that too XD too funny!

Answer 21

OMG, you wouldnt believe what i just did.
GUESS AND CHECK ALL THE WAY

Answer 22

0_o

Answer 23

and so far, the biggest area is with sides 90.9 and 135.65

Answer 24

Ooo nice.
I came up with 90.6666 and 136 for the side lengths.
So ya you're probably on the right track.

Answer 25

so
\[3x + 2y \le 544\]

Answer 26

You labeled the vertical lengths x?
AHHHH!!

Answer 27

>.<

Answer 28

yea. they should be the same lengths. two that are the same and three that are the same

Answer 29

then i graphed it and started pluggin points into that equation

Answer 30

well, I didn't think of doing that :/

Answer 31

Sorry I lost wifi!!!

Answer 32

But thank you so so much!

Answer 33

That makes total sense

Answer 34

youre welcome!