Question

The perimeter of a rectangular ranch is 400 m. Find the dimensions of the ranch that will contain the greatest area.

Answer 1

Wow every time i go to answer a question that i am incapable of answering you answer for me :)

Answer 2

so could be 50+50+100+100

Answer 3

could also be all 75

Answer 4

I am horrible at this stuff even though it looks very simple

Answer 5

500 or 150

Answer 6

do the 500 one

Answer 7

so 50+50+100+100

Answer 8

I know it's just a simple question but I just don't know how to start it.

Answer 9

it's an optimization problem

Answer 10

use the derivative to find the local maximum which in this case, the largest area

Answer 11

uhmmm, how? i don't know that @11calcBC

Answer 12

set x = length and y = width, u know that 2x + 2y = 400, so x =200 - y

Answer 13

implicit differentiation...

Answer 14

2(200 - y) + 2y = 400
400 - 2y + 2y = 400
400 = 400

Answer 15

is that right ?

Answer 16

well...it's right but plugging it in isn't solving it lol

Answer 17

u plug 200 - y into the area, so u get A(x) = (200-y)y

Answer 18

which you simplify to 200y - y^2

Answer 19

take the derivative of that, which is 200 - 2y

Answer 20

set that equal to 0, get ur critical point, which is 100 for y when you solve for it. remember to find the x value, which is 2x + 2(100) = 400, which is also equal to 100. also note that a number is the greatest when it's two values are the same

Answer 21

ur maximum area will then be 100 x 100 or 10,000

Answer 22

thank you so much for letting me understand and for helping me out with this :) @11calcBC :)

Answer 23

my pleasure :D