Question

The area of a rectangular garden is 289 square feet. The garden is to be enclosed by a stone wall costing $22 per linear foot. The interior wall is to be constructed with brick costing $9 per linear foot. Express the cost C, to enclose the garden and add the interior wall as a function of x.

Answer 1

the area of the rectangular garden is 289 square ft

so

`x* y=289`

so the value of y is 289/x

the outer perimeter of the garden is 2(x+y)

now perimeter is 2(x+289/x)

it is given that the outer wall cost 22 $ per linear foot

so the total cost is

`\begin{gathered} 22*2(x+(289)/(x)) \\ 22*(2x+(578)/(x)) \end{gathered}`

it is given that the cost of an interior wall is 9 $

and the length of the interior wall is x

the total cost of the interior wall is 9x

so the total cost of the wall is 9x +22 (2x + 578/x).

and the correct answer is 9x +22 (2x + 578/x). option B.