# If the area of a rectangle stays constant, what is the relationship between the base and the height?

## Question:

If the area of a rectangle stays constant, what is the relationship between the base and the height?

## Proportionality Between Variables:

We say that two variables are proportional if the ratio or their product is equal to a constant, known as the proportionality constant. There are two types of proportionalities: direct proportional and inverse proportional. For directly proportional variables, the ratio of the variables is equal to a constant. For inversely proportional variables, the product of the variables is equal to a constant.

The area of a rectangle is given by:

• {eq}A = l\times w {/eq}, where {eq}l {/eq} is the length and {eq}w {/eq} is the width of the rectangle.

If the area of the rectangle remains constant, then:

• {eq}l\times w = A = k {/eq}
• {eq}l\times w = k {/eq}

The relationship between the length and the width (the base) is that the {eq}\boxed{\color{blue}{\text{base and the length will be inversely proportional}}} {/eq} since their product is equal to a constant. 