Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

Sagot :

STEP 1:

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

[tex]\begin{gathered} w=\frac{2l}{3}\text{ where} \\ w\text{ = width} \\ l=\text{ length} \end{gathered}[/tex]

STEP 2:

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

[tex]\begin{gathered} \text{Perimeter = 2(l+w)} \\ 240=2(l+\frac{2l}{3}) \end{gathered}[/tex]

STEP 3:

Solve for l and subsequently w

[tex]\begin{gathered} \text{Perimeter}=\text{ 240 = 2(}\frac{2l+3l}{3})=2(\frac{5l}{3}) \\ 240=\frac{10l}{3} \\ \text{Cross multiplying gives 240}\times3=5l \\ l=\frac{240\times3}{10}=72ft \\ w=\frac{2l}{3}=\frac{2\times72}{3}=48ft \end{gathered}[/tex]

Therefore, length = 72 ft and width = 48ft

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.