Question

field #1
field #2
field #3
(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?

Explanation:

Step1: Find the width of each field

The perimeter of a rectangle is \(P = 2\times(\text{length}+\text{width})\). Given \(P = 12\) m.
For Field #1:
If length \(l_1=3\) m, then \(12 = 2\times(3 + w_1)\).
Divide both sides by 2: \(6=3 + w_1\).
Subtract 3 from both sides: \(w_1=6 - 3=3\) m.
For Field #2:
If length \(l_2 = 4\) m, then \(12=2\times(4 + w_2)\).
Divide both sides by 2: \(6 = 4+w_2\).
Subtract 4 from both sides: \(w_2=6 - 4 = 2\) m.
For Field #3:
If length \(l_3=5\) m, then \(12=2\times(5 + w_3)\).
Divide both sides by 2: \(6=5 + w_3\).
Subtract 5 from both sides: \(w_3=6 - 5=1\) m.

Step2: Find the area of each field

The area of a rectangle is \(A=\text{length}\times\text{width}\).
For Field #1: \(A_1=l_1\times w_1=3\times3 = 9\) \(m^2\).
For Field #2: \(A_2=l_2\times w_2=4\times2=8\) \(m^2\).
For Field #3: \(A_3=l_3\times w_3=5\times1 = 5\) \(m^2\).

Answer:

(a)

Field #1	Field #2	Field #3
Width	\(3\) m	\(2\) m	\(1\) m
Area	\(9\) \(m^2\)	\(8\) \(m^2\)	\(5\) \(m^2\)

(b) Field #1