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by Uva@90 » Tue Oct 22, 2013 7:41 am
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?
(1) Angles ABC and KLM are each equal to 55 degrees.
(2) LM is 6 inches.
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by mevicks » Tue Oct 22, 2013 8:08 am
Uva@90 wrote:The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?
(1) Angles ABC and KLM are each equal to 55 degrees.
(2) LM is 6 inches.
Given: A(ABC) = 4 * A(KLM)
Hypotenuse of KLM = 10

Q: Hypotenuse AB = ?

St1:
Angles ABC and KLM are each equal to 55 degrees. The two other angles are 90 (given that both are right triangles) and 35 (180 - 90 - 55).
Thus the triangles are similar and their areas would be in the same ratio as the ratio of the squares of their sides.
Thus we can find AB
SUFFICIENT

A(KLM)/A(ABC) = 1/4
1/4 = KL²/AB²
AB² = 4 * 100²
AB = 20

St2:
Now we can use the Pythagorean Triplet for the triangle KLM. Sides are KL = 10; LM = 6; KM = 8
Using this we can find the area of KLM and thus the area of ABC.
We know only about the area of ABC and thus its not sufficient to find out the length of hypotenuse AB
INSUFFICIENT

[spoiler]Answer: A[/spoiler]
Last edited by mevicks on Tue Oct 22, 2013 8:28 pm, edited 1 time in total.
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by Uva@90 » Tue Oct 22, 2013 8:59 am
mevicks wrote: Given: A(ABC) = 4 * A(KLM)
Hypotenuse of KLM = 10 thus the other two sides are 6 and 8 (Pythagorean triplets)
A(KLM) = (1/2)*6*8 = 24
A(ABC) = 4 * 24 = 96

Q: AB = ?


St1:
Angles ABC and KLM are each equal to 55 degrees
Thus the triangles are similar and their sides would be in the same ratio as the ratio of the squares of their areas.
Thus we can find AB
SUFFICIENT

St2:
This just repeats what is given.
INSUFFICIENT

[spoiler]Answer: A[/spoiler]
Hi Vivek,
Thanks for replying, I have couple of questions with your solution.

Firstly,
Hypotenuse of KLM = 10 thus the other two sides are 6 and 8 (Pythagorean triplets)
In the above statement how you came to conclusion that other sides or 6 and 8, Even it can be sqrt of (75) and sqrt(25) or sqrt (50) and sqrt (50) or what u mentioned as 6 and 8
In question nowhere they mentioned as integers right ?
So, could you pls clarify how you came to conclusion as 6 and 8.

Secondly,
Angles ABC and KLM are each equal to 55 degrees
Thus the triangles are similar and their sides would be in the same ratio as the ratio of the squares of their areas.
Here is what I understood from question,
Angle(ABC) and Angle(KLM) = 55 Degree.
or Angle B = Angle L = 55 Degree.
So, With one angle how you concluded both triangles are similar.
Please explain me what I understood is wright or wrong.


Thanks in advance,

Regards,
Uva.
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by mevicks » Tue Oct 22, 2013 8:28 pm
Hi Uva,

Thanks for pointing out the error related to pythogorean triplets, I've edited my post accordingly.

We need the question to explicitly state that the sides are integers to reach a conclusion outright that the other two sides are 6 and 8; so we cannot apply Pythagorean triplets initially.
Angle(ABC) and Angle(KLM) = 55 Degree.
or Angle B = Angle L = 55 Degree.
So, With one angle how you concluded both triangles are similar.
The stimulus states that the two triangles are "right triangles", so we can conclude that atleast one angle is 90°; St1 provides the value of the 2nd one thus we could find the value of the 3rd.
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by Uva@90 » Tue Oct 22, 2013 8:41 pm
The stimulus states that the two triangles are "right triangles", so we can conclude that atleast one angle is 90°; St1 provides the value of the 2nd one thus we could find the value of the 3rd.
Ah!!! That's the catch. Thanks for pointing out.
How many times I read still I couldn't get that(memory power gets decreasing,getting old :( )

Thanks Vivek.

Regards,
Uva.
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by ceilidh.erickson » Wed Oct 23, 2013 2:06 pm
Often in geometry DS questions, we can see what the GMAT is hinting at - all we need to do is to find the proof.

We're given that ABC and KLM are both right triangles, but we don't know what kind of right triangles, because we don't know any other angle measurements. We're told that the area of ABC is 4 times the area of KLM, which is a strong indication that these might be SIMILAR TRIANGLES. Similar triangles with an area ratio of 4:1 will have side length ratios of 2:1.

So we could think of the question as - are these similar triangles? If so, then the hypotenuse of ABC will be twice the hypotenuse of KLM.

Statement 1: If both triangles have a 55 degree angle, and both have a 90 degree angle, then they each have a 35 degree angle, too. They're similar! Sufficient

Statement 2: This gives us more about KLM, but doesn't allow us to compare anything about ABC. Insufficient.
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by ceilidh.erickson » Wed Oct 23, 2013 2:09 pm
Also, I just wanted to point out that this question has a factual inaccuracy...

Statement 2 allows us to conclude that KLM is a 6:8:10 triangle, but a 6:8:10 triangle (or any in a ratio of 3:4:5) would actually have degree measurements of approximately 37:53:90, not 35:55:90.

The GMAT will NEVER expect you to know this, but just FYI - do not memorize that a 35:55:90 is a 3:4:5, because that's not true.
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