Question

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 240 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. What is the length of the garden? The length of the garden is What is the width of the garden? The width of the garden is

Answer 1

STEP 1:

We'll derive an expression for the width and the length

`\begin{gathered} w=(2l)/(3)\text{ where} \\ w\text{ = width} \\ l=\text{ length} \end{gathered}`

STEP 2:

Next, We then derive an expression for the perimeter substituting w as a function of l

`\begin{gathered} \text{Perimeter = 2(l+w)} \\ 240=2(l+(2l)/(3)) \end{gathered}`

STEP 3:

Solve for l and subsequently w

`\begin{gathered} \text{Perimeter}=\text{ 240 = 2(}(2l+3l)/(3))=2((5l)/(3)) \\ 240=(10l)/(3) \\ \text{Cross multiplying gives 240}*3=5l \\ l=(240*3)/(10)=72ft \\ w=(2l)/(3)=(2*72)/(3)=48ft \end{gathered}`

Therefore, length = 72 ft and width = 48ft