Question

henry is going to use 32 m of fencing to fence off a rectangular field to grow vegetables. he is considering three fields with widths of 8 m, 9 m, and 10 m.
answer the questions below to find which of these fields would hold the most vegetables.
(a) fill in the table to find the length and the area for each field.
(b) which of these fields would hold the most vegetables?
field #1
field #2
field #3

Explanation:

Step1: Find the length of each field

We know that the perimeter of a rectangle is \(P = 2(l + w)\), and \(P=32\) m.
For Field #1: \(w = 8\) m. Using \(P = 2(l + w)\), we can solve for \(l\).
\(32=2(l + 8)\)
Divide both sides by 2: \(16=l + 8\)
Subtract 8 from both sides: \(l=16 - 8=8\) m.
For Field #2: \(w = 9\) m. Using \(P = 2(l + w)\)
\(32=2(l + 9)\)
Divide both sides by 2: \(16=l + 9\)
Subtract 9 from both sides: \(l=16 - 9 = 7\) m.
For Field #3: \(w = 10\) m. Using \(P = 2(l + w)\)
\(32=2(l + 10)\)
Divide both sides by 2: \(16=l + 10\)
Subtract 10 from both sides: \(l=16 - 10=6\) m.

Step2: Calculate the area of each field

The area of a rectangle is \(A=l\times w\).
For Field #1: \(A_1=8\times8 = 64\) \(m^{2}\)
For Field #2: \(A_2=7\times9=63\) \(m^{2}\)
For Field #3: \(A_3=6\times10 = 60\) \(m^{2}\)

Answer:

(a)

	Field #1	Field #2	Field #3
Length	\(8m\)	\(7m\)	\(6m\)
Width	\(8m\)	\(9m\)	\(10m\)

(b) Field #1