Question

kira is going to use 24 m of fencing to fence off a rectangular field to grow vegetables. she is considering three fields with lengths of 6 m, 7 m, and 8 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 formula for width

The perimeter of a rectangle is $P = 2\times(\text{length}+\text{width})$. Given $P = 24$ m, we can solve for width: $\text{width}=\frac{P}{2}-\text{length}$.

Step2: Calculate width and area for Field #1

• Width: $\frac{24}{2}-6=12 - 6=6$ m
• Area: $6\times6 = 36$ m²

Step3: Calculate width and area for Field #2

• Width: $\frac{24}{2}-7=12 - 7 = 5$ m
• Area: $7\times5=35$ m²

Step4: Calculate width and area for Field #3

• Width: $\frac{24}{2}-8=12 - 8 = 4$ m
• Area: $8\times4 = 32$ m²

Answer:

(a)

Length	Width	Area
7 m	5 m	35 m²
8 m	4 m	32 m²

(b) Field #1