Geometry Chapter 1 #15

by **sunilpunjabi** Fri Apr 25, 2008 2:31 pm

Sorry to post another question, but I’m getting lost on some of these solutions. Hopefully this is the right place and format for doing this.

In number 15 the area of the frame, larger square, is 6^2=36. I got that. Then the awswer goes on to state, the square inscribed in the frame is Â½ of 36 =18.
Where does the Â½ come from? I can not find anything in the questions that hints to this.
Again what am I missing?

Sunil

by **StaceyKoprince** Mon Apr 28, 2008 11:51 pm

This is absolutely the right place - no apologies necessary!

This line:
"The area of EFGH (for the picture) is equal to the area of the picture frame (the area of ABCD minus the area of EFGH)."

36 is actually NOT the area of the frame. It is the area of the frame plus the area of the picture. The frame is only the shell around the picture. So you'd have to take the entire area (36) and subtract the area of the picture in order to get the area of the frame.

Let Ap = area of the picture and Af = area of the frame.
Given:
Ap+Af = 36
Ap = Af

We can substitute and solve to get:
Ap = 18
Af = 18

Does that clear things up? I know it's confusing, but that wording is very similar to at least one real GMAT question I can think of...