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The area of triangle ABC

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The area of triangle ABC [#permalink] New post   31 May 2021, 04:16
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Attachment:
GRE The area of triangular region ABC.jpg
GRE The area of triangular region ABC.jpg [ 11.27 KiB | Viewed 3025 times ]



Quantity A
Quantity B
The area of triangular region ABC
The area of triangular region ADC



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The area of triangle ABC [#permalink] New post   31 May 2021, 19:32
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Let's say the perpendicular from B to AC is BM & from D to AC is DN

Area = \(\frac{1}{2} * base * perpendicular\)

To find the area we need to have those lengths. We are given BM = 5 but not given the dimension of DN.


Hence we can't find the area of triangle ADC.

Answer D
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Re: The area of triangle ABC [#permalink] New post   20 Jul 2021, 01:57
Carcass wrote:
Attachment:
GRE The area of triangular region ABC.jpg



Quantity A
Quantity B
The area of triangular region ABC
The area of triangular region ADC



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book



can someone please solve this problem for me?

thanking you in advance for your kidness
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Re: The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:27
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mrk9414 wrote:
Carcass wrote:
Attachment:
GRE The area of triangular region ABC.jpg



Quantity A
Quantity B
The area of triangular region ABC
The area of triangular region ADC



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book



can someone please solve this problem for me?

thanking you in advance for your kidness



Hi There!

In order to find the area of the triangle we need base and height. For the triangle above (ABC) we are given that the height is 5 and one of the side is 13 thus, using Pythagoras triplet we know the base will be 12+12=24

Now for the triangle below (ADC), we know the base is 24 but we do not know the height. Also we are not sure that angle ADC is 90 degrees to use the Pythagoras theorem to find the other side.

Thus, we only know are of one triangle and not the area of other

Therefore, the relationship cannot be determined.

IMO D

Let me know if you have further questions!

Hope this helps!
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The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:34
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Ks1859 wrote:
Hi There!

In order to find the area of the triangle we need base and height. For the triangle above (ABC) we are given that the height is 5 and one of the side is 13 thus, using Pythagoras triplet we know the base will be 12+12=24

Now for the triangle below (ADC), we know the base is 24 but we do not know the height. Also we are not sure that angle ADC is 90 degrees to use the Pythagoras theorem to find the other side.

Thus, we only know are of one triangle and not the area of other

Therefore, the relationship cannot be determined.

IMO D

Let me know if you have further questions!

Hope this helps!



thanks for your quick response.

but in triangle ADC it mentioned that a small triangle is 90 degrees then technically bigger part of the ADC should also be a right angle triangle.

as we have a hyp of small which might helps in finding the height of the triangle ?

why can't we do this?
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Re: The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:41
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mrk9414 wrote:

thanks for your quick response.

but in triangle ADC it mentioned that a small triangle is 90 degrees then technically bigger part of the ADC should also be a right angle triangle.

as we have a hyp of small which might helps in finding the height of the triangle ?

why can't we do this?



Okay, so lets say the height is DM. And we know one side is 90. Just for assumption, consider angle ADM=60 degrees, it is also possible that CDM is also 60 degrees in this case the angle corresponds to 120 degrees and is not a right angle. It could be a right angle triangle, but according to the given information, this assumption is a bit too wide to be made as this information is also open to other assumption.

And never trust the figures on GRE until and unless stated, as this is one of the best trick ETS uses to deceive.

Hope this helps!
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Re: The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:42
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Hey,

No assumptions should be there. Plus can you please share your way as I didn't understand
" technically bigger part of the ADC should also be a right angle triangle.
as we have a hyp of small which might helps in finding the height of the triangle ? "


mrk9414 wrote:

thanks for your quick response.

but in triangle ADC it mentioned that a small triangle is 90 degrees then technically bigger part of the ADC should also be a right angle triangle.

as we have a hyp of small which might helps in finding the height of the triangle ?

why can't we do this?
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mrk9414
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Re: The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:55
rx10 wrote:
Hey,

No assumptions should be there. Plus can you please share your way as I didn't understand
" technically bigger part of the ADC should also be a right angle triangle.
as we have a hyp of small which might helps in finding the height of the triangle? "


mrk9414 wrote:

thanks for your quick response.

but in triangle ADC it mentioned that a small triangle is 90 degrees then technically bigger part of the ADC should also be a right angle triangle.

as we have a hyp of small which might helps in finding the height of the triangle?

why can't we do this?



When it's mentioned that AMD is 90 degrees, technically CMD should also be 90 degrees. by triplet 30-60-90 we can find out the height "DM" to solve the problem . But, now I realise that It could also be right angle triangle or a special right-angle triangle (90-45-45).

Please share your opinion on this
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The area of triangle ABC [#permalink] New post   20 Jul 2021, 02:59
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All these are assumptions and as Ks1859 had pointed out, these all are tricks.

The triangle can be 30-60-90 ; 45-45-90 ; 10-80-90 or any other.

Consider all the figure with caution and do no make any assumptions unless the conditions are explicitly stated in the stem.

mrk9414 wrote:

When it's mentioned that AMD is 90 degrees, technically CMD should also be 90 degrees. by triplet 30-60-90 we can find out the height "DM" to solve the problem . But, now I realise that It could also be right angle triangle or a special right-angle triangle (90-45-45).

Please share your opinion on this
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