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What is the perimeter of isosceles triangle LMN? 1) Side LM

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by fskilnik@GMATH » Sun Sep 16, 2018 6:18 pm

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BTGmoderatorDC 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)

Source: Veritas Prep
\[{\Delta _{LMN}}\,\,{\text{isosceles}}\]
\[? = {\text{perim}}\left( {{\Delta _{LMN}}} \right)\]
\[\left( {1 + 2} \right)\]
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\[{\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,\operatorname{left} }} = 8 + 4\sqrt 2 \ne 4 + 8\sqrt 2 = {\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,{\text{right}}}}\]

We have presented a GEOMETRIC BIFURCATION for (1+2), therefore the right answer is [spoiler]__(E)___[/spoiler] .


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

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Sun Sep 16, 2018 6:33 pm

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Hi All,

We're told that triangle LMN is an isosceles triangle. We're asked for the PERIMETER of that triangle.

1) Side LM has a length of 4

With the information in Fact 1, we know that one (or possibly two) of the sides of this isosceles triangle, but we don't know all 3 sides, so the perimeter of the triangle could be more than one possible number.
Fact 1 is INSUFFICIENT

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

With the information in Fact 2, we know that one (or possibly two) of the sides of this isosceles triangle, but we don't know all 3 sides, so the perimeter of the triangle could be more than one possible number.
Fact 2 is INSUFFICIENT

Combined, we know...two of the sides - and that one of those numbers is the third side. That still leaves us with 2 possible values:
4 + 4 + sqrt{2}
or
4 + sqrt{2} + sqrt{2}
With two different possibilities for the perimeter, we don't know which one actually is the perimeter.
Combined, INSUFFICIENT

Final Answer: E

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by Brent@GMATPrepNow » Mon Sep 17, 2018 6:02 am

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BTGmoderatorDC wrote:What is the perimeter of isosceles triangle LMN?

1) Side LM has a length of 4

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

OA E

Source: Veritas Prep
Target question: What is the perimeter of isosceles triangle LMN?
Jump to. . . .

Statements 1 and 2 combined
There are two triangles that satisfy BOTH statements. They are:
Case a: The side lengths of triangle LMN are 4, 4 and 4√2. In this case, the answer to the target question is the perimeter = 4 + 4 + 4√2 = 8 + 4√2
Case b: The side lengths of triangle LMN are 4, 4√2 and 4√2. In this case, the answer to the target question is the perimeter = 4 + 4√2 + 4√2 = 4 + 8√2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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