geometry

sorry guys edited the q and i got the soln too.....its ADE/BCED

Ok, I got the answer.

So is it confirmed then that if two triangles are similar (acc. to the AA rule I applied here), then there altitudes are also similar???

Yes, if two triangles are similar, their altitudes are in the same proportion as their sides - as long as you are considering two matching altitudes in the two triangles.

thank you!

how you guys got this ? Can somebody please explain in detail.

Thanks.

ratio of area of two similar triangle is always square of the ratio of any two corresponding sides
---> Ar.of ABC/Ar. of ADE= ( BC/DE)^2=(5/3)^2
---->ABC/ADE = 25/9

(ADE+BCED)/ADE = 25/9

BCED/ADE = 16/9 or ADE/BCED = 9/16

hth

Can someone post a visual for this problem?

How we got BCED/ADE = 16/9 , basically BCED = 16 ??

Hi,

Here at Knewton, we have a saying in our GMAT prep course: DRAW A PICTURE. In order to quickly understand what is going on here, you need to understand that "BCDE" being a trapezoid MEANS that the line DE is parallel to the line BC. As it turns out, no sides in a triangle are EVER parallel to each other--the only way that you can really SEE this and thus recognize which lines are parallel is by drawing a picture.


Since DE is parallel to BC, you now know that you have a similar-triangles problem on your hands. Another little rule that we use at Knewton is that when you have a ratio of LINEAR measurements of the corresponding SIDES of two polygons (here triangles ADE and ABC have bases in the ratio 3:5), you know that the AREAS are going to be in the square of that ratio (i.e. the ratio of the area of triangle ADE to the area of triangle ABC will be 9:25). Nevermind worrying about altitudes, and bh/2, and confusing formulae.

But look out for the trap answer, A!! This question is asking for the ratio of the triangle ADE to the AREA OF THE TRAPEZOID. Since we're dealing with ratios here, with no absolute amounts, we can assume that the ratios of the areas will subtract in a nice way—subtract our representation of the area of triangle ADE (9) from the area of triangle ABC (25) to obtain a suitable representation of the area of the trapezoid BCDE (25 - 9 = 16). The ratio of the area of triangle ADE to the trapezoid BCDE is then 9:16. B is correct.

Thanks Josh, you are right, i should have drawn the pic, got it.

Josh: thanks for the drawing and clear explanation. Now you have me planning to seek more info about the ratios and linear mm of polygons.

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