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Two rectangles have the same breadth and the difference

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Two rectangles have the same breadth and the difference  [#permalink]

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New post 01 May 2012, 02:36
3
00:00
A
B
C
D
E

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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Re: Two rectangles have the same breadth....  [#permalink]

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New post 01 May 2012, 02:44
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
Answer "D"
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Re: Two rectangles have the same breadth and the difference  [#permalink]

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New post 03 Feb 2019, 00:18
1
breadth = b
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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Re: Two rectangles have the same breadth and the difference  [#permalink]

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New post 03 Feb 2019, 03:36
4d wrote:
breadth = b
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 ? :?
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Re: Two rectangles have the same breadth and the difference  [#permalink]

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New post 03 Feb 2019, 03:48
1
dave13 wrote:
4d wrote:
breadth = b
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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Re: Two rectangles have the same breadth and the difference   [#permalink] 03 Feb 2019, 03:48
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