a farmer has a rectangular garden plot surrounded by 240 feet of fence. find the length and width of the garden if it’s are is 2375 square-feet.

Question

a farmer has a rectangular garden plot surrounded by 240 feet of fence. find the length and width of the garden if it’s are is 2375 square-feet.

Answer 1

120 feet of fence makes the length and width

w represents the width

120 - w repressents the length

2375 = w(120 - w)

2375 = 120w - w²

w² - 120w + 2375 = 0

Can you solve for w and answer?

Answer 2

Hi, Karsyn!

For this question, the key is to set up a system of equations using our known values regarding the garden and then use those equations to solve for the length and width. First, we need to note that the two values that we are given are the area of the garden and the length of the fence surrounding it (which, mathematically speaking, gives us the perimeter of the garden). Therefore, we can use the general equations for perimeter and area to solve for length and width:

A = L•W, where A = area, L = length, and W = width

P = 2L + 2W, where P = perimeter

We can then plug in our values of A and P (A = 2,375ft², P = 240ft) into these equations and solve for L and W.

This should get you started, and from here on out it's just a matter of being careful with your algebra. I would recommend using the area equation to find L in terms of W (or vice versa), and then plugging that into the perimeter equation.

I hope this explanation was helpful, and please don't hesitate to reach out if you have any further questions!