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What is the area of the triangle ?

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What is the area of the triangle ?

by goelmohit2002 » Fri Sep 18, 2009 6:04 am
The below figure shows a right triangle in xy plane. If coordinate of A is (-15, 10), what is the area of triangle ABC ?
1) The coorinate of point B is (25, 25)
2) The coordinate of point C is (25,10)

[spoiler]OA = C. Can someone please tell can't we assume the right angle is at angle C. From figure it does not seem possible to have right angle anywhere else.[/spoiler]
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by kyabe » Fri Sep 18, 2009 6:25 am
I agree to you on this.. But one thing u need to keep in mind.. And that is : you can't assume anything on your own in DS, if it is not stated explicitly.. On that note I can say that Answer should be C. But again by looking at the diagram your reasoning seems correct as well.. BTW whats the source?
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by sunnyjohn » Fri Sep 18, 2009 6:27 am
Where did u get this Question...
Answer has to be A.

Use Pythagoras to prove yourself.

Please provide source and official explanation.
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by goelmohit2002 » Fri Sep 18, 2009 8:12 am
kyabe wrote:I agree to you on this.. But one thing u need to keep in mind.. And that is : you can't assume anything on your own in DS, if it is not stated explicitly.. On that note I can say that Answer should be C. But again by looking at the diagram your reasoning seems correct as well.. BTW whats the source?
actually if figure would not have been there...then surely yes...we can't assume....but figure is adding twist...

which one is correct here....should we assume angle c to be 90 or not ?
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by goelmohit2002 » Fri Sep 18, 2009 8:15 am
sunnyjohn wrote:Where did u get this Question...
Answer has to be A.

Use Pythagoras to prove yourself.

Please provide source and official explanation.
Actually I also tend to agree with you....but nowhere question say angle C is right angled.....

But in addition no other angle look to be right angled too :-(
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by kyabe » Fri Sep 18, 2009 9:21 am
DONT ASSUME ANYTHING
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Re: What is the area of the triangle ?

by gmat740 » Fri Sep 18, 2009 6:29 pm
goelmohit2002 wrote:The below figure shows a right triangle in xy plane. If coordinate of A is (-15, 10), what is the area of triangle ABC ?
1) The coorinate of point B is (25, 25)
2) The coordinate of point C is (25,10)

[spoiler]OA = C. Can someone please tell can't we assume the right angle is at angle C. From figure it does not seem possible to have right angle anywhere else.[/spoiler]

Please check the bold part of the question above. It is very important not to assume anything in DS questions but at the same time its important not to neglect minute details.
The question explicitly states that there is a right angle and by figure(which may not be drawn to scale) there is only one angle which seems to fit the bill.


Answer is C because...

1 => gives coordinate of hypotenuse, but we are not sure about the length of base and altitude. A could have been the answer if it were given that the triangle in Isosceles right angled triangle.


Hope this Helps
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by boy141 » Fri Sep 18, 2009 9:14 pm
In this problem, if you had another angle (30,60,90;60,60,60),

then you could find out the sides of the triangle. since we are giving 1 angle, WE CANNOT ASSUME that the other angles are 30 and 60.

Also, you could manipulate the image to make it into a 60,60,60 triangle with one point. you need all three points to figure out the area of this dumb thing.
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by aim-wsc » Sat Sep 19, 2009 10:19 am
We cannot assume <C to be 90 deg. since there's no sign in of rt angle in that figure. All we know is location of A & A forms a right angle triangle.

Since we're uncertain about which point has right angle, we need to know the coordinates of all three points.
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by boy141 » Sat Sep 19, 2009 11:33 am
aim-wsc wrote:We cannot assume <C to be 90 deg. since there's no sign in of rt angle in that figure. All we know is location of A & A forms a right angle triangle.

Since we're uncertain about which point has right angle, we need to know the coordinates of all three points.
::looks at the original question::

Oh snap! The figure doesn't have a right angle in it! Sorry. Then it is anything!! WE CAN'T ASSUME ANYTHING!
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by sanjib » Sat Sep 19, 2009 11:41 am
from all these it is very clear that the triangle is Right angle triangle because it is mentioned in the question stem itself.
Now as we know A and from st.1 B
we just cant assume that the C is right angled.So answer is C
But the problem started when it gives the drawing figure. we all are thinking that C is the one and only possible Right angle. But thats the mistake we made to answer.
How about the point B is making Right angle and A and C making Hypt. so we cant be sure without confirmation. and the confirmation only comes from St.2 therefore the only answer is C.
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by lunarpower » Thu Oct 01, 2009 3:01 am
whoa there people.

EVEN IF we assume that the right angle is at C, statement 1 is STILL not good enough to determine the area of the triangle.

even if we know that C is the right angle, all we know is the location of the hypotenuse. we have no reason to assume that the other two sides are parallel to the x- and y-axes.

there are LOTS of different right triangles with this side as hypotenuse - try drawing some. they'll have areas ranging all the way from approximately 0 (if point C is very close to A or B) to a maximum value (if the triangle is 45-45-90).

so yeah, that's still not sufficient. therefore, the issue of whether the right angle is located at C is immaterial; statement 1 is insufficient whether this is necessarily true or not.
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by lunarpower » Thu Oct 01, 2009 3:05 am
by the way, this question creates a REALLY bad precedent for the actual test.

in this problem, statements (1) and (2) together HAND YOU ALL THE INFORMATION IN THE PROBLEM, WITH NO WORK AT ALL. i.e., if you have BOTH of these statements, then you have all 3 points of the triangle, and there is nothing left to find out.

on the REAL exam, on problems like this (when the two statements together just hand you everything you need), the answer is very, very rarely C. (this is what we call a "c trap".)

if you have the 12th edition og, check out problems #60, 107, 136, 154, and 173 in the data sufficiency question. all are C traps. none have C as the correct answer.
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by goelmohit2002 » Thu Oct 01, 2009 3:54 am
Hi Ron,

Thanks !!!

What about statement 2 alone....is that sufficient ?

Thanks
Mohit
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by lunarpower » Thu Oct 01, 2009 4:08 am
goelmohit2002 wrote:Hi Ron,

Thanks !!!

What about statement 2 alone....is that sufficient ?

Thanks
Mohit
no. if you only have statement 2, then the vertical height of BC could be absolutely anything from 0 to infinity.
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