Question

using your math

1. the area of a rectangle is 18 square centimeters. if the length and width are both whole numbers, list all possible values for the length and width (assuming the length is the longer side). draw each rectangle.

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width, and $A = 18$ square - centimeters. We need to find all pairs of whole - number values for $l$ and $w$ such that $l\times w=18$.

Step2: Find factor pairs

We find the factor pairs of 18.
When $w = 1$ cm, $l=\frac{18}{1}=18$ cm.
When $w = 2$ cm, $l=\frac{18}{2}=9$ cm.
When $w = 3$ cm, $l=\frac{18}{3}=6$ cm.
Since the length is the longer side, we don't consider the reverse cases (e.g., $w = 18$ and $l = 1$ etc. as we have already accounted for them with the length being the longer side).

Answer:

Length (cm)	Width (cm)
9	2
6	3