MGMAT CAT: Similar Triangles

[aaa]

http://www.manhattangmat.com/OnlineExam ... ID=1295783

Please see link for diagram.

I am having trouble with similar triangles. For example, how does one figure out that "the longer leg of right triangle BDE is DE and the corresponding leg in ABD is BD, not DA.

I have bolded the line I am referring to below. Thank you for all of your help.


In the diagram to the right, what is the length of AB?

(1) BE = 3

(2) DE = 4

We are given a right triangle that is cut into four smaller right triangles. Each smaller triangle was formed by drawing a perpendicular from the right angle of a larger triangle to that larger triangle's hypotenuse. When a right triangle is divided in this way, two similar triangles are created. And each one of these smaller similar triangles is also similar to the larger triangle from which it was formed.

Thus, for example, triangle ABD is similar to triangle BDC, and both of these are similar to triangle ABC. Moreover, triangle BDE is similar to triangle DEC, and each of these is similar to triangle BDC, from which they were formed. If BDE is similar to BDC and BDC is similar to ABD, then BDE must be similar to ABD as well.

Remember that similar triangles have the same interior angles and the ratio of their side lengths are the same. So the ratio of the side lengths of BDE must be the same as the ratio of the side lengths of ABD. We are given the hypotenuse of BDE, which is also a leg of triangle ABD. If we had even one more side of BDE, we would be able to find the side lengths of BDE and thus know the ratios, which we could use to determine the sides of ABD.

(1) SUFFICIENT: If BE = 3, then BDE is a 3-4-5 right triangle. BDE and ABD are similar triangles, as discussed above, so their side measurements have the same proportion. Knowing the three side measurements of BDE and one of the side measurements of ABD is enough to allow us to calculate AB.

To illustrate:
BD = 5 is the hypotenuse of BDE, while AB is the hypotenuse of ABD.
The longer leg of right triangle BDE is DE = 4, and the corresponding leg in ABD is BD = 5.

Since they are similar triangles, the ratio of the longer leg to the hypotenuse should be the same in both BDE and ABD.
For BDE, the ratio of the longer leg to the hypotenuse = 4/5.
For ABD, the ratio of the longer leg to the hypotenuse = 5/AB.

Thus, 4/5 = 5/AB, or AB = 25/4 = 6.25

(2) SUFFICIENT: If DE = 4, then BDE is a 3-4-5 right triangle. This statement provides identical information to that given in statement (1) and is sufficient for the reasons given above.

The correct answer is D.

[GMAT 2007]

Dude, There is some problem with the link..

GMAT 2007

[StaceyKoprince]

yep - please see my response to your other post in which you attempted to link to your private practice center. You need to grab a screenshot and use an image hosting service to post the image.