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What is the perimeter of isosceles triangle LMN?

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What is the perimeter of isosceles triangle LMN? [#permalink]

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New post 15 Feb 2016, 13:09
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What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4

(2) Side MN has a length of \(4\sqrt{2}\)
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What is the perimeter of isosceles triangle LMN? [#permalink]

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New post 15 Feb 2016, 16:27
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zxcvbnmas wrote:
What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4

(2) Side MN has a length of \(4\sqrt{2}\)

Dear zxcvbnmas,
I'm happy to respond. :-)

First of all, as you may know, this is a Veritas question. Also, as you may know, any math question from any reasonably popular source is likely already to be posted here. This question already has a long thread here:
in-isosceles-triangle-lmn-what-is-the-measure-of-angle-n-205668.html
Technically, my friend, you have violated the norms of the GMAT Club forum by opening a brand new thread for a question rather than adding your question to the thread already in existence. Always search for a question before starting a new thread. Presumably, Bunuel will merge this thread into that one.

Briefly, I will say that, even if we know both statements, we don't know which side is repeated. The triangle could have sides
(a) 4 and 4 and \(4\sqrt{2}\) -- an Isosceles Right Triangle, i.e. a 45-45-90 triangle
or
(b) 4 and \(4\sqrt{2}\) and \(4\sqrt{2}\) -- an acute isosceles triangle

Because we can't determine between these, the answer is (E).

Does all this make sense?

Mike :-)
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Re: What is the perimeter of isosceles triangle LMN? [#permalink]

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New post 16 Aug 2016, 22:38
mikemcgarry : The link you have posted has a similar question, but there is a difference in the prompt. This question asks for perimeter whereas the other question asks for measure of an angle.

Coming back to this question, Option A & B individually are insufficient. But when combined, the side LM has a length 4 and MN has length 4 root 2. Since it is mentioned that it is an isosceles triangle, either it can be 4,4 & 4 root 2 or 4, 4 root 2 & 4 root 2. Either ways, the perimeter would be equal, right.?

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What is the perimeter of isosceles triangle LMN? [#permalink]

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narendran1990 wrote:
mikemcgarry : The link you have posted has a similar question, but there is a difference in the prompt. This question asks for perimeter whereas the other question asks for measure of an angle.

Coming back to this question, Option A & B individually are insufficient. But when combined, the side LM has a length 4 and MN has length 4 root 2. Since it is mentioned that it is an isosceles triangle, either it can be 4,4 & 4 root 2 or 4, 4 root 2 & 4 root 2. Either ways, the perimeter would be equal, right.?

Dear narendran1990,

I'm happy to respond. :-)

My friend, the number \(4\sqrt{2}\) is a number on the number line, a number very different from 4. Since \(\sqrt{2} \approx 1.4\), we know that \(4\sqrt{2} \approx 4 \times 1.4 = 5.6\).

Think about the two triangles in this light:

Triangle #1 has sides 4, 4, and 5.6
Triangle #2 has sides 4, 5.6, and 5.6

These two triangles do not have the same perimeter, and both are possible, given the two statements.

Does all this make sense?
Mike :-)
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Re: What is the perimeter of isosceles triangle LMN? [#permalink]

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New post 02 Mar 2017, 15:31
When can we use the proportions of triangles then? I thought that since we know 4 and 4sqr2, we can use the X:X:Xsqr2 proportions! so we know the perimeter

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What is the perimeter of isosceles triangle LMN? [#permalink]

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New post 15 Nov 2017, 00:55
zxcvbnmas wrote:
What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4

(2) Side MN has a length of \(4\sqrt{2}\)



narendran1990 and iliavko

Hello I was just attempting this question and at first I thought the exact same that the both statements once combined we can get the perimeter.

But the rule x:x:x\(\sqrt{2}\) is for right angle isosceles since no where in the question stem is stated that it is a right angle, the sides could be

either 4, 4\(\sqrt{2}\), 4\(\sqrt{2}\)
or 4 , 4, 4\(\sqrt{2}\)

Thus the perimeter can be either 8\(\sqrt{2}\)+4 or 8 + 4\(\sqrt{2}\)

Which makes C incorrect, hence, the answer is E.

I hope this clarifies it .

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What is the perimeter of isosceles triangle LMN?   [#permalink] 15 Nov 2017, 00:55
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