What is the perimeter of isosceles triangle LMN?

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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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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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

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 .

\({\Delta _{LMN}}\,\,{\text{isosceles}}\)

\(? = {\text{perim}}\left( {{\Delta _{LMN}}} \right)\)

\(\left( {1 + 2} \right)\) See image attached.

\({\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,\operatorname{left} }} = 8 + 4\sqrt 2 \ne 4 + 8\sqrt 2 = {\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,{\text{right}}}}\)


We have presented a GEOMETRIC BIFURCATION for (1+2), therefore the right answer is (E).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4

(2) Side MN has a length of 4√2

Detail Solution -

Here given triangle MLN is isosceles triangle , that means, any 2 sides of 3 sides are same in length and any 3 angles of 3 angles are same. we don't have idea about which sides and which angles are same.. Here asking for preimeter of triangle ...that is sum of sides.

Hence ,
Information -1 : Side LM has length 4....we don't have idea about rest sides..and also not telling this side is one of 2 sides which are same...hence this is not sufficient.
Inforomation -2 : Side MN has length 4√2,....same..other details are not available...as first. Not sufficient

Now 1+2

LM = 4, MN = 4√2 , NL =?????....P = LM+MN+NL
but given triangle is isosceles...hence 2 sides are equal in length...that means...eithere NL = LM or NL = MN ...hence NL has 2 values possible..so perimeter has also 2 values possible..

Hence Option C also not sufficient.
A,B,C,D rejected....Only Option E is correct.

Hope if you liked solution, please appreciate with Kudos.

C-trap problem...I missed it this time, but here's the solution.

What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4
Clearly insufficient. The two equivalent sides can be 4 or the remaining side can be 4.

(2) Side MN has a length of 4√2
Clearly insufficient. The two equivalent sides can be 4√2 or the remaining side can be 4√2.

C: Still insufficient

We don't know whether the two equal sides are 4 or 4√2 so we get different perimeters.
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