If ABCD is a rectangle, what is the area of the shaded region?

Hi All,

When the GMAT puts a right triangle in front of you, it is probably NOT a random right triangle. While there are some exceptions, in most cases, you're looking at a 3/4/5, 5/12/13, 30/60/90 or 45/45/90 right triangle. If you see ANY clues that point to a specific right triangle, then you should think about how you can prove that the triangle IS what you think it is.

Here, we have 3 right triangles and they all appear to be multiples of a 3/4/5 (notice how each has a diagonal that is a MULTIPLE of 5).

Assuming they're all 3/4/5s, the sides SHOULD be....

Big triangle: 15/20/25
Middle triangle: 12/16/20
Small triangle: 9/12/15

From the picture, there are a couple of other things that need to "line up" to prove that we're correct:

1) One side of the "small" and "middle" triangles MUST be the same.
2) The "other" sides of each of those triangles MUST add up to 25 (the diagonal of the big triangle)

The common "shared" side would be 12, which means the "other" sides (16 and 9) add up to 25. So we have the EXACT situation that we thought we did. With knowledge of ALL of the side lengths, we can now answer any question that's asked.

GMAT assassins aren't born, they're made,
Rich