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Math Expert V
Joined: 02 Sep 2009
Posts: 53864
What is the perimeter of a rhombus? (1) Its area is 140 square meter  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 66% (00:44) correct 34% (01:09) wrong based on 50 sessions

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What is the perimeter of a rhombus?

(1) Its area is 140 square meters
(2) One of its diagonals is 48 meters

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CEO  P
Joined: 18 Aug 2017
Posts: 2502
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the perimeter of a rhombus? (1) Its area is 140 square meter  [#permalink]

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1
Bunuel wrote:
What is the perimeter of a rhombus?

(1) Its area is 140 square meters
(2) One of its diagonals is 48 meters

diagnoal of rhombus bisect at 90* and adjacents sides are equal so if we know diagonal length we can find perimeter

from 1
area of rhombus : 0.5 * d1*d2

d1*d2= 280

d1 and d2 not know

in sufficient

from 2
d1 = 48
so two sides would be
2x^2= 48
x^2=24
x= 2 sqrt6

we dont know other two sides so in sufficient

from 1 & 2

d2* 48= 280

d1= 5.8 ~ 6
so other two sides

2x^2= 6
x^2= 3
x= sqrt 3 = ~1.7 = ~ 2

so perimeter = 2 * ( 2+ 2 sqrt6 )= 2* ~7 = 14
IMO C
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Director  D
Joined: 27 May 2012
Posts: 718
Re: What is the perimeter of a rhombus? (1) Its area is 140 square meter  [#permalink]

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Archit3110 wrote:
Bunuel wrote:
What is the perimeter of a rhombus?

(1) Its area is 140 square meters
(2) One of its diagonals is 48 meters

diagnoal of rhombus bisect at 90* and adjacents sides are equal so if we know diagonal length we can find perimeter

from 1
area of rhombus : 0.5 * d1*d2

d1*d2= 280

d1 and d2 not know

in sufficient

from 2
d1 = 48
so two sides would be
2x^2= 48
x^2=24
x= 2 sqrt6

we dont know other two sides so in sufficient

from 1 & 2

d2* 48= 280

d1= 5.8 ~ 6
so other two sides

2x^2= 6
x^2= 3
x= sqrt 3 = ~1.7 = ~ 2

so perimeter = 2 * ( 2+ 2 sqrt6 )= 2* ~7 = 14
IMO C

Hi Archit3110,
Thank you for your solution But I am unable to get the following part,May be I am missing something,
Archit3110 wrote:

d1 = 48
so two sides would be
2x^2= 48
x^2=24
x= 2 sqrt6

How do we know that the two adjacent sides form a 90 Deg. angle to use Pythagoras theorem. I assume you meant to write $$2x^2= 48^2$$, where x is one side of a rhombus. Also if we knew X, shouldn't we know all the sides of the rhombus as in a Rhombus all the sides are equal.

Thank you.
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- Stne
CEO  P
Joined: 18 Aug 2017
Posts: 2502
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the perimeter of a rhombus? (1) Its area is 140 square meter  [#permalink]

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1
stne wrote:
Archit3110 wrote:
Bunuel wrote:
What is the perimeter of a rhombus?

(1) Its area is 140 square meters
(2) One of its diagonals is 48 meters

diagnoal of rhombus bisect at 90* and adjacents sides are equal so if we know diagonal length we can find perimeter

from 1
area of rhombus : 0.5 * d1*d2

d1*d2= 280

d1 and d2 not know

in sufficient

from 2
d1 = 48
so two sides would be
2x^2= 48
x^2=24
x= 2 sqrt6

we dont know other two sides so in sufficient

from 1 & 2

d2* 48= 280

d1= 5.8 ~ 6
so other two sides

2x^2= 6
x^2= 3
x= sqrt 3 = ~1.7 = ~ 2

so perimeter = 2 * ( 2+ 2 sqrt6 )= 2* ~7 = 14
IMO C

Hi Archit3110,
Thank you for your solution But I am unable to get the following part,May be I am missing something,
Archit3110 wrote:

d1 = 48
so two sides would be
2x^2= 48
x^2=24
x= 2 sqrt6

How do we know that the two adjacent sides form a 90 Deg. angle to use Pythagoras theorem. I assume you meant to write $$2x^2= 48^2$$, where x is one side of a rhombus. Also if we knew X, shouldn't we know all the sides of the rhombus as in a Rhombus all the sides are equal.

Thank you.

stne
area of rhombus = 1/2 * d1 * d2 ; d1 & d2 are two diagonal of rhombus which bisect each other at 90*..
using this relation I used to solve #1...
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Director  D
Joined: 27 May 2012
Posts: 718
Re: What is the perimeter of a rhombus? (1) Its area is 140 square meter  [#permalink]

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Ok, I figured it out,though I did not quite get your working
Basically we can divide the Rhombus in 4 right triangles. Then lets take one right triangle , it will have legs of 24 and approx 3 and hypotenuse equal to Side of a Rhombus. So we can calculate a side of Rhombus and hence the perimeter.

Thanks.
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- Stne Re: What is the perimeter of a rhombus? (1) Its area is 140 square meter   [#permalink] 07 Mar 2019, 06:40
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# What is the perimeter of a rhombus? (1) Its area is 140 square meter

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