geometry

Question

In a triangle ABC,pt. D is on side AB nd point E is on side AC. BECD is a trapezium.. DE:BC=3:5. calculate the ratio of the area of 
ADE and BCED ?

a)9/25
b)9/16
c)27/125
d)3/5
e)12/25

OA  b)

Acc3ss · Answer

Are you sure everything in this question is right ??

according to me, answer should be 25:16

ADE:BCED = 9:16

gmatdelhi · Answer

even i got 25:16...but, I think we're wrongly assuming that if 2 triangles are similar, their altitudes must also be proportionate. But, I don't know what the correct rule to apply here is! Somebody explain?

xcusemeplz2009 · Answer

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

gmatdelhi · Answer

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???

IanStewart · Answer

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.

gmatdelhi · Answer

thank you! <img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" />

tashu · Answer

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

Thanks.

xcusemeplz2009 · Answer

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

gottabwise · Answer

Can someone post a visual for this problem?

rohitsb · Answer

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

JoshKnewton · Answer

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.

Attachment:

GMAT geo.gif [ 3.71 KiB | Viewed 3042 times ]

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.

rohitsb · Answer

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

gottabwise · Answer

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.

Posted from my mobile device

geometry

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards