Areas and Perimeters

[baily106]

Hello,

I've pulled this question from NOVA's Great Math Prep Course. It is an example they used to discuss hard quantitative comparisons, but there explanation wasn't very clear. It states that Column A has the area of a square with perimeter 12. Column B has the area of a parallelogram with perimeter 16. Which is bigger? The answer provided is D stating that looking at various cases both can be bigger. Could you tell me in which cases column A would be bigger?

Thanks.

[tommywallach]

Hey Baily,

Well, this certainly wouldn't qualify as that difficult a question, if it makes you feel better!

The area of a square with perimeter 12 is defined (you can't try multiple things). It has sides of 3, and an area of 9.

The parallelogram's area can actually shrink down to just bigger than zero. Think of it this way, imagine that two of the parallel sides have length of 7.99999999999. That would mean the other parallel sides are .0000000000001 long. So the height would be tiny, and the area would also be tiny.

Make sense?

-t

[baily106]

I think where I ran into trouble here is that I was trying to find the height in the parallelogram for different scenarios. It sounds like one doesn't necessarily have to find the height for each case for the parallelogram, but instead make the assumption that because the sides can get as tiny as .0000000000001, then the height would also be tiny, correct? However, would it be possible to find the height of the parallelogram in this case? If so, how would one do that?
Thanks.

[tommywallach]

Hey Baily,

Yep. There's no need to actually "solve" for anything, so I wouldn't worry about it. You can't really do it anyway (because the height of the parallelogram is dependent on the angle that the "base" makes with the diagonals).

-t

[baily106]

Ok, that is what I was getting stuck on: trying to find the height.
It makes sense.
Thank you.

[tommywallach]

Glad to help!

-t