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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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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]
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]
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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Re: What is the perimeter of isosceles triangle LMN? [#permalink]
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 $$4\sqrt{2}$$

$${\Delta _{LMN}}\,\,{\text{isosceles}}$$

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

$$\left( {1 + 2} \right)$$ 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.
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16Set18_8b.gif [ 21.69 KiB | Viewed 11808 times ]

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