Question

4.The length of a rectangular picture frame has been found to be an irrational number. Dwayne says that, because the length is an irrational number, the perimeter and area would always be irrational. Using complete sentences, critique Dwayne’s statement with examples that demonstrate how he is correct or incorrect.

Answer 1

Let A and B be irrational numbers

Then to find the area we would do A * B
To find the perimeter we would do 2 * A + 2 * B
So do you know if there is any way that the area or perimeter would be a rational number?

Answer 2

Well if I put in any numbers that make it rational, such as perfect squares, and they add/multiply to a rational number, either perimeter or area could right?

Answer 3

Well the Area could, because you would be multiplying lets say \[\sqrt{2}*\sqrt{2}\] which would get you 2. but if you tried that with the perimeter you would get \[2*\sqrt{2}+2*\sqrt{2} = 4*\sqrt{2}\]

Answer 4

Oh okay. So if the length is an irrational number(says the question) the width could either be rational or irrational. So the area could be rational but the perimeter would be irrational?

Answer 5

If the length (and or width) is irrational then the area could be rational because
\[\sqrt{2}*\sqrt{2}=2\]But then the perimeter can never be rational.

Answer 6

So the area may or may not be rational but the perimeter could never be rational.

Answer 7

Would that be the answer for the question?

Answer 8

Yup.

Answer 9

Okay thank you so much!

Answer 10

Your welcome!