Question

My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. Find the total cost of the fencing as a function of the length of a side x.

Answer 1

The total cost of the fencing as a function of side is
`C = 8\cdot x`.

Explanation:

Dimensionally speaking, the total cost is equal to the product of length and cost per length. Given that orchid garden has a square form, there is only an input: Side (
`x`), measured in feet. Therefore, the total cost of fencing is represented by the following formula:

`C = (c_(west) + c_(south) + c_(east))\cdot x`

Given that
`c_(west) = c_(east) = 2\,(\$)/(ft)` and
`c_(south) = \$\,4\,(\$)/(ft)`, the total cost of the fencing as a function of side is:

`C = 8\cdot x`