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# A triangular park needs to be wired along its boundary.

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Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
A triangular park needs to be wired along its boundary.  [#permalink]

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11 Jan 2019, 22:49
1
1
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Difficulty:

25% (medium)

Question Stats:

68% (01:01) correct 32% (01:19) wrong based on 27 sessions

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A triangular park needs to be wired along its boundary. Which of the following can be the total length of the wire required if lengths of the two sides of the park are 4m and 7m?

I. 16m
II. 21m
III. 23m

A. I only
B. II only
C. I& II only
D. II& III only
E. I,II& III
Intern
Joined: 15 Dec 2018
Posts: 30
Re: A triangular park needs to be wired along its boundary.  [#permalink]

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12 Jan 2019, 00:32
C

If perimeter is 23, the third side will be 12 which is against the below rule

The sum of any 2 sides in a triangle has to be greater than the third side.

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VP
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: A triangular park needs to be wired along its boundary.  [#permalink]

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12 Jan 2019, 00:44
akurathi12 wrote:
A triangular park needs to be wired along its boundary. Which of the following can be the total length of the wire required if lengths of the two sides of the park are 4m and 7m?

I. 16m
II. 21m
III. 23m

A. I only
B. II only
C. I& II only
D. II& III only
E. I,II& III

Sum of 2 sides > than the third side, and the difference of 2 sides should be < third side

I. 16m, third side = 5, 11 > 5 & 4 < 5, satisfies
II. 21m, third side = 10, 11 > 10 & 4 < 10, satisfies
III. 23m, third side = 12, 11 > 12(Not possible) & 4 < 12, Doesn't satisfy

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Math Expert
Joined: 02 Aug 2009
Posts: 7757
Re: A triangular park needs to be wired along its boundary.  [#permalink]

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12 Jan 2019, 00:53
akurathi12 wrote:
A triangular park needs to be wired along its boundary. Which of the following can be the total length of the wire required if lengths of the two sides of the park are 4m and 7m?

I. 16m
II. 21m
III. 23m

A. I only
B. II only
C. I& II only
D. II& III only
E. I,II& III

In such questions, find the extremes

(I) Minimum perimeter..
for this find the LEAST possible dimension of the third side..
THIRD side will be GREATER than the DIFFERENCE of the other two sides.. THIRD side > (7-4), so Perimeter >7+4+(7-4).....P>14

(I) Maximum perimeter..
for this find the GREATEST possible dimension of the third side..
THIRD side will be SMALLER than the SUM of the other two sides.. THIRD side < (7+4), so Perimeter <7+4+(7+4).....P<22

so $$14<perimeter<22$$

I and II are in the range but II is not..

C
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Re: A triangular park needs to be wired along its boundary.   [#permalink] 12 Jan 2019, 00:53
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