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655-705 Level|   Geometry|      
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mikemcgarry
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 15 Aug 2014, 13:04
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C
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55% (hard)

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61% (02:00) correct 39% (01:54) wrong based on 161 sessions

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mahendru1992
If AD = 10\(\sqrt{3}\) and ADC is a right angle, what is the area of triangle ABC?

(1) AC = 20

(2) \(angle BAD=30^{\circ}\)

This was asked in the Kaplan free test, but I think that the answer is wrong.

Am I wrong (most probably I am, lol). If I am, what's wrong with what i did?
Dear mahendru1992,
I'm happy to respond. :-)

See this blog for some information about what you can and can't assume.
https://magoosh.com/gmat/2012/gmat-trick ... -possible/
That article is about assumptions in the PS questions. In the GMAT DS, you can make absolutely no assumptions from the diagram.

One very easy assumption blatantly encouraged by the diagram is that triangle is symmetrical. This erroneous assumption was your starting point. ABC is drawn to appear isosceles, but there is absolutely nothing in the prompt information that guarantees that it is isosceles --- for all we know, triangle ABD and triangle ADC are completely different, and have nothing in common except for a right angle. It is very tempting to assume symmetry, but that is absolutely something you are allowed to assume, even on the GMAT PS. On the GMAT DS, you can assume nothing.

Does all this make sense?
Mike :-)
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mikemcgarry
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 15 Aug 2014, 13:39
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mahendru1992
But Mike I was under the impression that a perpendicular drawn from the vertex of a triangle to the base divides the triangle into 2 similar ones? O.o
My friend, that's only true for isosceles triangles. On these very special triangle, see:
https://magoosh.com/gmat/2012/isosceles- ... -the-gmat/
Not all triangles are so special.
Attachment:
asymetrical triangle.JPG
asymetrical triangle.JPG [ 19.17 KiB | Viewed 3923 times ]
In asymmetrical triangle, nothing is shared between the two halves except the right angle and the length of AD.
Does this make sense?
Mike :-)
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 24 Sep 2014, 13:37
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Hi Experts,

Can someone explain me how do we get C?
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 24 Sep 2014, 13:52
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maggie27
Hi Experts,

Can someone explain me how do we get C?
Maggie,
I'm happy to help. :-)

To understand this, you must understand about the 30-60-90 triangle, and it's special properties:
https://magoosh.com/gmat/2012/the-gmats- ... triangles/
and you must understand in detail the magic of isosceles triangles:
https://magoosh.com/gmat/2012/isosceles- ... -the-gmat/

Statement #1 makes the right triangle, ADC, a 30-60-90 triangle, but tells us nothing about the left.
Statement #2 makes the left triangle ADB, a 30-60-90 triangle, but tells us nothing about the right.

Together, they are congruent 30-60-90 triangles, so we can find all lengths and solve for the area. That's the gist, and with the information in those two blogs, you should be able to work out the details.

Does all this make sense?
Mike :-)
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 24 Sep 2014, 15:33
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maggie27
Hi Experts,

Can someone explain me how do we get C?
Maggie,
I'm happy to help. :-)

To understand this, you must understand about the 30-60-90 triangle, and it's special properties:
https://magoosh.com/gmat/2012/the-gmats- ... triangles/
and you must understand in detail the magic of isosceles triangles:
https://magoosh.com/gmat/2012/isosceles- ... -the-gmat/

Statement #1 makes the right triangle, ADC, a 30-60-90 triangle, but tells us nothing about the left.
Statement #2 makes the left triangle ADB, a 30-60-90 triangle, but tells us nothing about the right.

Together, they are congruent 30-60-90 triangles, so we can find all lengths and solve for the area. That's the gist, and with the information in those two blogs, you should be able to work out the details.

Does all this make sense?
Mike :-)


Thanks Mike,
So can I even apply of isosceles triangle property(a perpendicular will divide the opposite side into 2 equal parts?) now that I have got that this triangle is isosceles using stmt 1 and stmt 2 together?
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 24 Sep 2014, 16:19
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maggie27
Thanks Mike,
So can I even apply of isosceles triangle property(a perpendicular will divide the opposite side into 2 equal parts?) now that I have got that this triangle is isosceles using stmt 1 and stmt 2 together?
Dear Maggie,
Well, with both statements, you don't even need that property. If we have two 30-60-90 triangles that share the corresponding side, that instantly means that both triangles are congruent and identical in their measurements. The fact that the perpendicular divides them into two congruent triangles is also true, but here a consequence of what we want, not a cause of it.
Does this make sense?
Mike :-)
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If AD = 10*3^(1/2) and ADC is a right angle, what is the area of 13 Apr 2022, 04:41
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