Question

ivan is going to use 12 m of fencing to fence off a rectangular field to grow vegetables. he is considering three fields with lengths of 3 m, 4 m, and 5 m. answer the questions below to find which of these fields would hold the most vegetables. (a) fill in the table to find the width 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 width of each field

The perimeter of a rectangle is \(P = 2(l + w)\). Given \(P=12\)m.
For Field #1 (\(l = 3\)m):
\(12=2(3 + w)\)
\(6=3 + w\)
\(w = 3\)m.
For Field #2 (\(l = 4\)m):
\(12=2(4 + w)\)
\(6=4 + w\)
\(w = 2\)m.
For Field #3 (\(l = 5\)m):
\(12=2(5 + w)\)
\(6=5 + w\)
\(w = 1\)m.

Step2: Find the area of each field

The area of a rectangle is \(A=l\times w\).
For Field #1 (\(l = 3\)m, \(w = 3\)m):
\(A=3\times3 = 9\)m².
For Field #2 (\(l = 4\)m, \(w = 2\)m):
\(A=4\times2 = 8\)m².
For Field #3 (\(l = 5\)m, \(w = 1\)m):
\(A=5\times1 = 5\)m².

Answer:

Field #1	Field #2	Field #3
Area: \(9\)m²	Area: \(8\)m²	Area: \(5\)m²

(b) Field #1 would hold the most vegetables as it has the largest area (\(9\)m²).