Math questions from any Manhattan Prep GMAT Computer Adaptive Test.
bruno.torres.gomez
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Trapezoid In Triangle

by bruno.torres.gomez Sun Mar 20, 2011 5:59 am

In one of the MGMAT CAT tests, i found this

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?
.A
/ \
B/___ \ E
/ \
c---------D

... using proportions > AD = 8

In the answer, it states ->

Triangle CAD is a right triangle since it has side lengths of 6, 8 and 10, which means that triangle BAE is also a right triangle (they share the same right angle).

Can the sides determine the type of triangle ? (in this case, it is a triangle rectangle because of 6,8 and 10) i read somewhere, that it cannot ? So, if i see a triangle 2,1,1*sqrt(3) , then it must be a 30-60-90 ?

Please do let me know
Very much appreciated .

Bruno
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Re: Trapezoid In Triangle

by jnelson0612 Sun Mar 20, 2011 3:21 pm

Bruno, can you please post an image for this problem?
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Re: Trapezoid In Triangle

by bruno.torres.gomez Mon Mar 21, 2011 12:46 am

Hi,

Thanks for your reply!
Please see the image here (http://postimage.org/image/2gqmzti3o/)
Image
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Re: Trapezoid In Triangle

by tim Mon Mar 21, 2011 8:46 am

yes, if you have the three side lengths - or even the ratio of side lengths - you can determine all the angles of a triangle. in particular, if the sides of the triangle satisfy the Pythagorean Theorem you can conclude that the triangle is a right triangle..
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Re: Trapezoid In Triangle

by bruno.torres.gomez Mon Mar 21, 2011 12:07 pm

thank you guys!
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Re: Trapezoid In Triangle

by jnelson0612 Fri Apr 01, 2011 1:01 pm

Thanks! :-)
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Re: Trapezoid In Triangle

by rgaddam Mon Apr 18, 2011 11:15 pm

tim Wrote:yes, if you have the three side lengths - or even the ratio of side lengths - you can determine all the angles of a triangle.


Can you please give me an example or two for the above statement so that I can better understand the concept.

Thanks
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Re: Trapezoid In Triangle

by tim Tue Apr 26, 2011 2:00 pm

Bruno already gave you two examples..
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Re: Trapezoid In Triangle

by dandarth1 Sun Sep 02, 2012 2:52 pm

The problem I am having with this question is, why are we assuming that ADC is a triangle at all? It looks like a triangle, but AB and AE also look like they are equivalent lengths, which they are not. So couldn't BC and ED skew off into different directions while still maintaining the parallel nature of BE and CD? Because I didn't know why we should make these assumptions, I guessed. I thought we were always supposed to assume that the picture is not drawn to scale.
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Re: Trapezoid In Triangle

by RonPurewal Wed Sep 05, 2012 3:18 am

dandarth1 Wrote:The problem I am having with this question is, why are we assuming that ADC is a triangle at all? It looks like a triangle, but AB and AE also look like they are equivalent lengths, which they are not. So couldn't BC and ED skew off into different directions while still maintaining the parallel nature of BE and CD? Because I didn't know why we should make these assumptions, I guessed. I thought we were always supposed to assume that the picture is not drawn to scale.


in any diagram -- whether it's to scale or not -- you can always assume the following:

* straight lines are straight lines

* points are actually connected in the order shown (e.g., if three points on a line are in the order a-b-c, then that's their actual order -- they are not, say, a-c-b in "real life")

these are bare-minimum assumptions. without these, ALL diagrams would be completely worthless. (think about it for a second -- if what you're saying here is a consideration, then anything that looks like a triangle could actually be, say, an octagon.)

the point of "not to scale" diagrams is that the sizes of things -- lengths, angles, etc. -- can be distorted. however, the very nature of lines, etc. will not be misrepresented.
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Re: Trapezoid In Triangle

by jwagambill Wed Dec 19, 2012 2:54 pm

I have an issue with this. In order for BE and CD to be parallel, how can ED and BC be different lengths? Would this not indicate that BE and CD are not parallel?
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Re: Trapezoid In Triangle

by jlucero Sat Dec 22, 2012 12:34 am

jwagambill Wrote:I have an issue with this. In order for BE and CD to be parallel, how can ED and BC be different lengths? Would this not indicate that BE and CD are not parallel?


Nope. It depends on the angles that the non-parallel sides form. Note that the non-parallel sides of the right trapezoid are of different length b/c they form different angles with the right side of the figure.
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Re: Trapezoid In Triangle

by griffin.811 Sun Sep 07, 2014 7:59 pm

I apologize in advance because I'm pretty sure this is a simple oversight on my part, but how do we know the height of either triangle here?

Thanks
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Re: Trapezoid In Triangle

by RonPurewal Mon Sep 08, 2014 8:51 pm

If a right triangle is considered with either of the two perpendicular sides as "base", then "height" is the other one of the two.

(Normally, "height" must be drawn into the diagram perpendicular to "base". If two sides are already perpendicular, though, there's no need for any auxiliary constructions.)
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Re: Trapezoid In Triangle

by griffin.811 Tue Sep 09, 2014 12:13 pm

Perfect. I wasn't sure whether or not the hypotenuse could be considered the base as well.

Thanks Ron