Question

A rectangle has an area of 36 square units. As the length and the width change, what do you know about their product? Is this length proportional to the width? Justify your reasoning.

Answer 1

Area = 36 = length*width

Then, while the area is constant the product length*width is constant.

Length and area are inversely related.

That means that to keep the same product (area), length vary in inverse proportion to width.

If you increase length, widht has to decrease to satisfy this relation:

width = 36/length

Of course, you can also say: length = 36 / width.