If the perimeter of a rectangle is 14 inches, then its area is 10 square inches.

## counterexample

# 3 Answers

I take it you're supposed to provide a rectangle with a perimeter of 14 inches but an area that is not 10 inches?

Easy enough. What are the side lengths that would make the perimeter 14 inches? You're only going to have two lengths, because for each side, there is one side that is the same length, or else it's not a rectangle.

Find a list of side lengths that will, when pushed through the area formula, give an area that's not 10 square inches.

Julie, you will see the term "counterexample" throughout the year. It means to provide an example that proves the hypothosis false. For example, "All bunnies have ears. Fluffy has ears. Therefore Fluffy is a bunny." The counterexample is that fluffy could be any animal with ears that is not a bunny, such as a dog.

David provided a great example for your perimeter/area question, but I wanted to make sure you knew other questions will come up using this same logic/reasoning.

Factor 14 as a product of two integers. There is more than one way. You'll see that one way gives area 10 so pick an alternative.

## Comments

David give the best answer by NOT giving an actual counter-example but a method to find them. Howeer, just to be sure I think we math folks should tell Julie that these are whole number counters; s1 = 4, s2 = 3; or ht = 1 and base = 6. The only Example I can think of is s1=5, s2=2.Comment