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Intern  Joined: 27 Sep 2011
Posts: 13
Two rectangles have the same breadth and the difference  [#permalink]

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Difficulty:   15% (low)

Question Stats: 92% (02:34) correct 8% (03:34) wrong based on 37 sessions

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Two rectangles have the same breadth and the difference between their perimeters is 56m. If the difference between their areas is 336m^2, find the breadth of the rectangles.

A. 18
B. 10
C. 24
D. 12

Source: Mathematics by L.Harwood Clarke ( page: 168, No.11)

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Intern  Joined: 25 Apr 2012
Posts: 10
Re: Two rectangles have the same breadth....  [#permalink]

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Let the common breadth be 'b'
and lengths be x and y
Diff. of perimeters = 2(x+b) - 2(y+b) = 2(x-y) = 56
=> x-y = 28
Diff. of areas = bx - by = b(x-y) = 336
=> b = 336/28 = 12
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Ravi Sankar Vemuri
Manager  G
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: Two rectangles have the same breadth and the difference  [#permalink]

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1
Length of first rectangle = x
Length of first rectangle = y

Difference in perimeters $$= 2(x+b) - 2(y+b) = 2(x-y) = 56 \rightarrow x-y = 28$$
Difference in areas $$= bx - by = b(x-y) = 336 \rightarrow b = 336/28 = 12$$

IMO D
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VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: Two rectangles have the same breadth and the difference  [#permalink]

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4d wrote:
Length of first rectangle = x
Length of first rectangle = y

Difference in perimeters $$= 2(x+b) - 2(y+b) = 2(x-y) = 56 \rightarrow x-y = 28$$
Difference in areas $$= bx - by = b(x-y) = 336 \rightarrow b = 336/28 = 12$$

IMO D

4d
how did you get 28 ? Manager  G
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: Two rectangles have the same breadth and the difference  [#permalink]

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1
dave13 wrote:
4d wrote:
Length of first rectangle = x
Length of first rectangle = y

Difference in perimeters $$= 2(x+b) - 2(y+b) = 2(x-y) = 56 \rightarrow x-y = 28$$
Difference in areas $$= bx - by = b(x-y) = 336 \rightarrow b = 336/28 = 12$$

IMO D

4d
how did you get 28 ? dave13

$$2(x+b)−2(y+b)=2x+2b-2y-2b =2x-2y=2(x−y)=56$$

$$2(x−y)=56$$ [divide by 2]
$$x-y=28$$
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KUDOS will increase your score Re: Two rectangles have the same breadth and the difference   [#permalink] 03 Feb 2019, 03:48
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