The quantities, and the type of proportionality observed would be:
- a.) The time to drive 100 miles and average driving speed are inversely proportional.
- b.) The lengths of sides of a rectangle with a fixed perimeter are not inversely proportional.
- c.) The lengths of sides of a rectangle with a fixed area are inversely proportional.
How to find the proportionality ?
If you increase your average driving speed, it takes less time to cover the same distance of 100 miles. Conversely, if you decrease your speed, it takes more time.
To determine if the given quantities are inversely proportional, we need to understand what inversely proportional means. Two quantities are inversely proportional if one quantity increases when the other decreases, and the product of the two quantities remains constant.
The area A of a rectangle is calculated as A = l * w . If the area is constant and you increase the length, you must decrease the width w proportionately to maintain the same area, and vice versa.
This relationship is an example of inverse proportionality since the product of l and w (which is the area) remains constant.
The full question is:
Are these two quantities inversely proportional? a.) The time it takes to drive 100 miles and the average driving speed b.) The lengths of sides of a rectangle if the perimeter is fixed c.) The lengths of sides of a rectangle if the area is fixed