Question

21.) A rectangle has an area of 36 square units. As the length and width change, what do you know about their

product? is the length proportional to the width? Justify your reasoning.
Aren
Rectangle Length
width
3
12
36
36
Reminder: Area is the number of square units INSIDE a polygon.
To find area of a rectangle multiply length by width.

Answer 1

the length and the width are inversely proportional to each other (
`l=(36)/(w)` or
`w=(36)/(l)`)

Explanation:

Let

l units = length of the rectangle,

w units = width of the rectangle.

The area of the rectangle is

`\text{Area}=\text{Length}\cdot \text{Width}`

A rectangle has an area of 36 square units, so

`l\cdot w=36`

Complete the table with some values of l and w that fit the previous formula:

`\begin{array}{ccc}\text{Length}&\text{Width}&\text{Area}\\ \\36&1&36\cdot 1=36\ un^2.\\18&2&18\cdot 2=36 \ un^2.\\12&3&12\cdot 3=36\ un^2.\\ 9&4&9\cdot 4=36\ un^2.\\l&w&l\cdot w=36 \ un^2.\end{array}`

As you can see, the length and the width are inversely proportional to each other (
`l=(36)/(w)` or
`w=(36)/(l)`)