Question

1. a rectangle has a perimeter of 36 units.

a. create a table that shows the length and width of at least 3 different rectangles that also have a perimeter of 36 units.
b. describe the relationship between the columns of your table.

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $P$ is perimeter, $l$ is length and $w$ is width. Given $P=36$, we have $36 = 2(l + w)$, which simplifies to $l + w=18$.

Step2: Generate table values

When $l = 1$, $w=18 - 1=17$; when $l = 2$, $w = 18- 2=16$; when $l=3$, $w=18 - 3 = 15$; when $l = 4$, $w=18-4 = 14$; when $l=5$, $w=18 - 5=13$; when $l = 6$, $w=18-6=12$; when $l=7$, $w=18 - 7 = 11$; when $l=8$, $w=18-8 = 10$; when $l = 9$, $w=18-9=9$.

Length ($l$)	Width ($w$)
2	16
3	15
4	14
5	13
6	12
7	11
8	10
9	9

Step3: Describe relationship

The sum of the length and the width in each row is always 18. As the length increases by 1 unit, the width decreases by 1 unit. The length can be considered the independent variable and the width is the dependent variable since the value of the width depends on the value of the length according to the equation $w=18 - l$.

Answer:

a.

Length ($l$)	Width ($w$)
2	16
3	15
4	14
5	13
6	12
7	11
8	10
9	9

b. The sum of length and width in each row is 18. As length increases by 1, width decreases by 1. Length is independent variable and width is dependent variable with $w = 18 - l$.