Question

a rectangle has a perimeter of 30 units.
a. create a table that shows the length and width of at least 3 different rectangles that also have a perimeter of 30 units.
b. describe the relationship between the columns of your table.
c. write an equation to represent the relationship. identify the independent and dependent variables.

Explanation:

Step1: Recall perimeter formula

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

Step2: Create the table

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

Step3: Describe the 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 to keep the perimeter constant.

Step4: Write the equation and identify variables

The equation is $w = 18 - l$. The independent variable is $l$ (the length), and the dependent variable is $w$ (the width) since the value of the width depends on the value of the length.

Answer:

a. See the table above.
b. The sum of length and width in each row is 18. As length increases, width decreases to keep perimeter constant.
c. Equation: $w = 18 - l$. Independent variable: $l$. Dependent variable: $w$.