GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 22:58 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In a triangle ABC, Point D is on side AB and point E is on side AC,

Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 01 Jun 2015
Posts: 194
Location: India
GMAT 1: 620 Q48 V26
In a triangle ABC, Point D is on side AB and point E is on side AC,  [#permalink]

### Show Tags

1
8 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:21) correct 32% (02:59) wrong based on 66 sessions

### HideShow timer Statistics

In a triangle ABC, Point D is on side AB and point E is on side AC, such that BCDE is a trapezium. If DE: BC=3:5 then Calculate the ratio of the area of ΔADE and that of trapezium BCED.

A.3:4
B.9:16
C.3:5
D.9:25
E.5:9
Math Expert V
Joined: 02 Aug 2009
Posts: 8753
Re: In a triangle ABC, Point D is on side AB and point E is on side AC,  [#permalink]

### Show Tags

1
1
techiesam wrote:
In a triangle ABC, Point D is on side AB and point E is on side AC, such that BCDE is a trapezium. If DE: BC=3:5 then Calculate the ratio of the area of ΔADE and that of trapezium BCED.

A.3:4
B.9:16
C.3:5
D.9:25
E.5:9

Hi,
what you get is Triangle ABC and triangle ADE as two similar triangle..where ABC is the larger triangle..
RATIO of areas is SQUARE of sides of two triangles..

SO Area of ADE/Area of ABC = $$(\frac{3}{5})^2 = \frac{9}{25}$$ = 9x/25x...

But area of BCDE = area of ABC - Area of ADE = 25x-9x = 16x..
so Area of ADE/Area of BCDE = $$\frac{9x}{16x}$$ = 9/16...
B
_________________
Manager  B
Joined: 08 Aug 2015
Posts: 55
Re: In a triangle ABC, Point D is on side AB and point E is on side AC,  [#permalink]

### Show Tags

I solved this in the following manner: (I am assuming the folks reading this have drawn the appropriate figure)

Let the height of triangle ADE be x and the height of the trapezium be y
Now, let's assume that 3 and 5 are the actual lengths of sides DE and BC respectively

The area of triangle ADE is 1/2*3x
The area of trapezium DECB is 1/2*(3+5)y i.e., 1/2*8y

The ratio of their areas is thus: 3x/2 divided by 8y/2

This gives us: 3x/8y.

Now look through the options and see which one of the values given can possibly fit this expression. 'B' is the only one!
Non-Human User Joined: 09 Sep 2013
Posts: 15382
Re: In a triangle ABC, Point D is on side AB and point E is on side AC,  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: In a triangle ABC, Point D is on side AB and point E is on side AC,   [#permalink] 21 Apr 2019, 08:09

# In a triangle ABC, Point D is on side AB and point E is on side AC,  