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# M04 #12

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Senior Manager
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10 Oct 2009, 17:14
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Since the triangle has ABC as a right triangle, the square of the triangle would be multiple of two non hypothenuse sides of the triangle divided by two.
Statement ! just provides us with the information about the measurement of side AB
Not sufficient.

Hence, we know that 2) The product of the non-hypotenuse sides is equal to 24, which is multiple of sides AB and BC (reuqired sides)
We can conclude that Statement 2 is sufficient to answer the question.

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11 Oct 2009, 01:30
Question here,

When they said that DB is the hight of ABC (right triangle) that means DB intersects with AC (hypotenuse), then is DB perpendicular on AC??
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13 Oct 2009, 03:59
rshawabka wrote:
Question here,

When they said that DB is the hight of ABC (right triangle) that means DB intersects with AC (hypotenuse), then is DB perpendicular on AC??

Hi there

yes, this is a geometry theorem
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21 Oct 2009, 18:25
Yes,
If it says hight it is always perpendicular to the side which it crosses.
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21 Oct 2009, 18:59
IMO B

S2 gives product of AB and BC (which are non-hypotenuse sides).

is there any catch ? whats the OA?
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25 Oct 2009, 02:33
Whats the OA?
Stmt 1: Quesrie: doesn't BD bisect AC? then,AD=AC....hmm?
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07 Nov 2009, 00:31
Point D is crucial to solve this question as it is used to identify the non-hypotenuse sides (AB and BC)

Thus, B is the best for me
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08 Nov 2009, 16:31
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The point D is a misleading trap here. You don't need that information.

Rt Triangle ABC - What's AB *BC - or one leg * hypotenuse

Statement 1 - not enough clearly

Statement 2 - product of two legs given,
using the theorm hypotenuse^2 = leg1^2 + leg2^2
leg1 *leg2 = 24.

Asked to find leg1*hypotenuse. From the above two equations it can easily be determined. Hence B is sufficient.
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19 Jan 2010, 19:13
Could someone post a diagram? I think that would help me a lot. I don't understand where "D" is coming from either.
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22 Mar 2010, 08:59
Take a look at the diagram here: http://en.wikipedia.org/wiki/Right_triangle

As per wikipedia, there are 3 ways to calculate the area of a right triangle:

"As with any triangle, to calculate the area, multiply the base and the corresponding height, and divide it by two. If ABC is a right triangle in A, each of the sides [AB] and [AC] can be considered as the height; the base is then the other side of the right angle ([AC] and [AB], respectively)."

Finally: "The area of the triangle could also be calculated by using the hypotenuse as the base. One would then have to calculate the height associated with the hypotenuse, as it would no longer be one of the sides."

Therefore, in the picture in wikipedia, besides using the legs, the only other way to draw a "height" of the triangle is to draw a line from the right angle vertex (A) to the hypotenuse (BC).

Same logic would apply in this problem.
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25 Mar 2010, 00:31
aelfred wrote:
"If distinct points A, B, C, and D form a right triangle ABC with a height BD, what is the value of AB times BC?"

The language of this question appears at odds with the author's intent.

With respect to a triangle, the word "height" really only means "a line segment perpendicular to a triangle's edge, of a length equal to the distance of that edge from the opposite vertex." Height BD may or may not land D on the perimeter of the triangle. A line segment labeled "height" may just as easily be outside the triangle as inside the triangle, and is indeed outside the triangle in one example from a Grade 6 math text. "Height" means whatever helps you calculate the area of a triangle most easily; GMAC's OG12 does not use this term.

The term "altitude" would make the answer explanation work. From OG12 p.130: "The altitude of a triangle is the segment drawn from a vertex perpendicular to the side opposite that vertex." D must then lie on the perimeter of right triangle ABC, and B must be opposite the hypotenuse AC for D to be distinct from A and C.

Since GMAC does apparently regard "altitude" as fair game on the exam, and even gives the area of a triangle as "0.5*(base plus altitude)" on OG12 p.130, is there any chance of having this question amended to refer to "altitude BD" rather than "height BD" for future M04 takers?

Since the stimulus states the triangle ABC is a right triangle, D must lie on one of the sides.

also,
One might assume the following,
If we draw the right triangle ABC with D lieing on AC.
S1 tells us that AB = 6. Since this is a right triangle, then the other sides are 8 and 10 by using the pythagorean triples 3-4-5. (use a factor of 2)

However,
the sides could also be 2.5, 6, 6.5 using the pyth. triple of 5-12-13 (use a factor of 1/2)

Therefore S1 is not sufficient.
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03 Jul 2010, 02:21
If distinct points A ,B ,C , and D form a right triangle ABC with a height BD , what is the value of AB times BC ?

1. AB =6
2.The product of the non-hypotenuse sides is equal to 24.

I got it wrong because of the language/wording "what is AB times BC"
Does it mean AB*BC?
or value of AB is how much times BC?

Is this correct wording or language???? Both meaning changes the answer
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03 Jul 2010, 06:50
assume one of the non hyp sides is AB = x. then the other side AC = 24/x because the product of the two sides 24.

using these two sides - the hypotenuse BC = sqrt(x^2 + [24/x]^2)
We are required to find AB times BC which IMO is AB*BC
x*sqrt(x^2 + [24/x]^2)

But we don't know the value of x. A gives the value of x. So IMO the ans should be D - we need both choices to answer the question. I am not sure how B could be right.

Even if AB times BC means AB/BC we still can't do without taking both choices into consideration
because then we would have to calculate
x/sqrt(x^2 + [24/x]^2)
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06 Jul 2010, 22:09
If you draw the triangle you will see that AB and BC are the 2 short sides of the right triangle. You are asked for AB*BC, but stmt 1 doesn't say anything about BC. Stmt 2 instead gives you exactly the answer (you can read it as AB*BC=24). That's why the answer is B!
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06 Jul 2010, 23:55
Thanks guys
i just got confused with the wording
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20 Jul 2010, 05:07
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This is a tricky one
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20 Jul 2010, 05:11
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Since all points are distinct and BD is the height...D lies on AC and AC is hypotenueus.
The right angle is formed at B.
In all other scenarios, D equals either A/C

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20 Jul 2010, 05:12
I am missing something. Can someone tell me how a triangle can have 4 distinct points, A,B,C,D? Can someone please sketch the question so that I can see the triangle visually?
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20 Jul 2010, 06:00
I just subscribed to the daily question. I was wondering where everyone obtains the possible answer choices for the quant questions?

Thanks!
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20 Jul 2010, 06:05
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hope this will help
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Re: M04 #12   [#permalink] 20 Jul 2010, 06:05

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# M04 #12

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