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
What is the perimeter of isosceles triangle LMN? 1) Side LM
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
\[{\Delta _{LMN}}\,\,{\text{isosceles}}\]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
\[? = {\text{perim}}\left( {{\Delta _{LMN}}} \right)\]
\[\left( {1 + 2} \right)\]
\[{\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,\operatorname{left} }} = 8 + 4\sqrt 2 \ne 4 + 8\sqrt 2 = {\left[ {{\text{perim}}\left( {{\Delta _{LMN}}} \right)} \right]_{\,{\text{right}}}}\]
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.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: What is the perimeter of isosceles triangle LMN?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
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
Cheers,
Brent