1. ## Word Problem

Hi, everyone. i'm new here. I hope someone can help me this. I really am not good in word problem.

Janice wants to fence in a small garden area next to a stream.If she has 20 feet of fencing materials and doesn't fence the side bordering the stream, find the dimensions that will yield the maximum area and then find the maximum area she can enclose.

2. Originally Posted by Vkenny
Hi, everyone. i'm new here. I hope someone can help me this. I really am not good in word problem.

Janice wants to fence in a small garden area next to a stream.If she has 20 feet of fencing materials and doesn't fence the side bordering the stream, find the dimensions that will yield the maximum area and then find the maximum area she can enclose.
did you draw a diagram? let the side parallel the stream be x and the two sides perpendicular the stream be y.

note that we have x + 2y = 20 amount of fence.

the area is given by A = xy. this is what we want to maximize

can you continue?

3. Originally Posted by Jhevon
did you draw a diagram? let the side parallel the stream be x and the two sides perpendicular the stream be y.

note that we have x + 2y = 20 amount of fence.

the area is given by A = xy. this is what we want to maximize

can you continue?
i should do like this

x+y=20
x=20-2y then
A=(20-2y)
is this right

4. Originally Posted by Vkenny
i should do like this

x+y=20
x=20-2y then
A=(20-2y)
is this right
no, if x = 20 - 2y and A = x*y, how do you get A = 20 - 2y, wouldn't that be the same as saying A = x, which we know is not true?

5. Originally Posted by Jhevon
no, if x = 20 - 2y and A = x*y, how do you get A = 20 - 2y, wouldn't that be the same as saying A = x, which we know is not true?
so i need to find a value of x and y in order to find the area.

6. Originally Posted by Vkenny
so i need to find a value of x and y in order to find the area.
A = y(20 - 2y)

this is a downward opening parabola. find the y-value of its vertex, that gives you the maximum. then you can find the corresponding x-value

7. Originally Posted by Jhevon
A = y(20 - 2y)

this is a downward opening parabola. find the y-value of its vertex, that gives you the maximum. then you can find the corresponding x-value
I'm sorry. i still didnt know how to solve this. how do you find y value.

8. Originally Posted by Vkenny
I'm sorry. i still didnt know how to solve this. how do you find y value.
see post #4 here

9. Originally Posted by Jhevon
see post #4 here
is this right
Y=5
x=10
then i completed the square
A=-2(y-5)^2+25

10. Originally Posted by Vkenny
is this right
Y=5
x=10
yes

then i completed the square
A=-2(y-5)^2+25
nope, it is $-2(y - 5)^2 + 50$

11. thank you so much. i understand it now.h