What is the perimeter of isosceles triangle LMN?

Question

1) Side LM has a length of 4

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

mikemcgarry · Accepted Answer

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 :-)

narendran1990 · Answer

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.?

mikemcgarry · Answer

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 imes 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 :-)

iliavko · Answer

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

Salsanousi · Answer

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 .

fskilnik · Answer

{\Delta _{LMN}}\,\,{	ext{isosceles}}

? = {	ext{perim}}\left( {{\Delta _{LMN}}} ight)

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

{\left _{\,\operatorname{left} }} = 8 + 4\sqrt 2 
e 4 + 8\sqrt 2 = {\left _{\,{	ext{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.

JiddiHuMain · Answer

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.

CEdward · Answer

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.

bumpbot · Answer

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What is the perimeter of isosceles triangle LMN?

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What is the perimeter of isosceles triangle LMN?

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