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What are the areas of the two triangles formed by extending

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Dan
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What are the areas of the two triangles formed by extending [#permalink] New post   26 Sep 2004, 23:14
00:00
A
B
C
D
E

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(N/A)

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0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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What are the areas of the two triangles formed by extending the legs of a trapezoid until they intersect?

1. Area of trapezoid = 100, bases 6 and 14.
2. Height of trapezoid = 10.



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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 00:48
E.

1. Insuff. Area of trapezium = 1/(sum of parallel sides) x height. =>100=1/2(6+14)xh. =>h=10. Not enough info to determine the area of two triangles.

2. Insuff. Gives the same info as above.

Together, still insufficient. Hence E.
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 02:17
If i got the picture right : A.

T = area of trapezoid.
x = small base
y = large base
H= Height of Big triangle
h= Height of Small triangle

We know that T + x*h/2 = y*H/2

Statement A: T=100, x=6, y=14.
So
100 + 6*h/2 = 14*H/2.

We also know that 100=(x+y)*(H-h).
100=20(H-h)
H=5+h.

With those Two equations we will find h and H, which were missing to answer the question.
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 02:26
A pic would be very useful in this case...

h is the small height, H the big one

h/H=6/14

H-h=10

Answer is C
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 02:38
3 different answers we got here.
It might be a GMAT-CLUB record :)
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 02:54
You are right Dookie, except for prob questions ;-)

I would be interested in having some more opinions on this one...
I used Thales theorem, maybe i had a too simple vision of the stuff...
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 05:05
I was thinking the question stem is asking for the areas of ABC and ADE

Note that BCDE is the trapezium. See the illustration.

Dookie, I understand your first equation. I think the second equation should be 100= 1/2(x+y)(H-h). I seem to have completely neglected the first equation. I agree with A.
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trapezium.JPG [ 8.96 KiB | Viewed 3726 times ]

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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 06:12
C is the answer.
Reason : The formula for calculating the area of trapezium is valid if and only if the bases are parallel, ( think of it , what shall be the altitude of the bases are not parallel )
Now once we take both statements into account we can see that the trapezium indeed has parallel bases. ( If the alt is 10 and sum of bases is 20 then the only way it can have an area of 100 is if it was a trapezium with parallel bases. )
Now of course use similarity of triangles and find out the soultion ..
Thus the catch is that just from A yu can't assume the altitude is 10 cuz the concept of altitude does not exist UNTIL the bases r parallel.
Yu need B to confirm that it indeed it has parallel bases. Thereafter the solution is as proposed earlier.
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 07:12
Dookie, Fantastic!!

The second equation should be 100=(x+y)*(H-h)/2.

Yes..it is A


Dookie wrote:
If i got the picture right : A.

T = area of trapezoid.
x = small base
y = large base
H= Height of Big triangle
h= Height of Small triangle

We know that T + x*h/2 = y*H/2

Statement A: T=100, x=6, y=14.
So
100 + 6*h/2 = 14*H/2.

We also know that 100=(x+y)*(H-h).
100=20(H-h)
H=5+h.

With those Two equations we will find h and H, which were missing to answer the question.
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 08:52
You are right dookie, first statement is enough to find height...

Good catch !
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   27 Sep 2004, 22:37
A is the answer. Could be solved as Dookie did (with 1/2 added), or using a bit geometry.

the 2 triangles are similar (you figure why), so the sides are in proportions. let h be the height of the smaller triangle, and H of the larger.

h/6 = (h+10)/14 and you get h and then the areas. That is it. Simple!
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   28 Sep 2004, 00:23
Is a trapezoid an isoceles trapezium or ? ..There is an answer C available above which talks about parallel bases. Confused...
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Re: What are the areas of the two triangles formed by extending [#permalink] New post   28 Sep 2004, 00:43
I concur, i made a mistake .
The answer is A since a trapezium by definition has parallel sides :)
I do need to study a bit....took so many things so lightly .



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Re: What are the areas of the two triangles formed by extending [#permalink]
28 Sep 2004, 00:43
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