What is the perimeter of isosceles triangle LMN?

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.?

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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