Manhattan Prep Geo - p. 92 #13

[Alexander]

Hi -

The wording is getting to me again, especially in the explanation, which states:

" The area of the frame and the area of the picture sum to the total area of the image, which is 36" - I get this because they tell us AB is 6.

" Therefore, the area of the frame and the picture are each equal to half of 36, or 18. Since EFGH is a square, the length of EF is sq-root(18) "

The blue section is where I get lost.

- Area of the frame + picture = 36
- Why does are each equal to half? Can't one be 20 an the other 16?
- I'm lost where the sq-root(18) is coming from.

Thanks,
Alexander

[tommywallach]

Hey Alexander,

Nice and simple this time. The question actually TELLS you that the area of the picture is equal to the area of the frame. They HAVE to be the same (so one can't be 16 and the other 20). If they're both the same, then they both equal half of the total area of the whole thing (picture + frame).

Hope that makes sense!

-t