Question

I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $128 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose?

Answer 1

let x = length and y = height, so we might have something like this

Answer 2

The fencing for the east and west sides costs $4 per foot

so it costs 4y + 4y = 8y dollars to do the east and west sides

Answer 3

the fencing for the north and south sides costs only $2 per foot

so it costs 2x+2x = 4x dollars to do the north and south sides

Answer 4

In total, it will cost you 4x + 8y dollars to do the whole enclosure

Answer 5

Your budget is $128, so let's say you spend exactly that much money (nothing more, nothing less)

Answer 6

this would mean

4x + 8y = 128

Answer 7

Solve for x or y and tell me what you get

Answer 8

it might make sense to solve for y, but either one works

Answer 9

like this? y=16-.5x

Answer 10

good

Answer 11

keep that in mind because we'll use that later

Answer 12

now the area of this rectangle



is

A = Length * Width

A = LW

A = x*y