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The square region shown has been partitioned into 5 identical rectangu

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The square region shown has been partitioned into 5 identical rectangu [#permalink]

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New post 13 Jul 2016, 17:29
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Question Stats:

72% (01:22) correct 28% (01:56) wrong based on 128 sessions

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The square region shown has been partitioned into 5 identical rectangular regions. If the perimeter of each of the rectangular regions is 30, what is the perimeter of the square region?

A) 150
B) 146
C) 120
D) 50
E) 46

[Reveal] Spoiler:
Attachment:
Screen Shot 2016-07-14 at 02.25.10.png
Screen Shot 2016-07-14 at 02.25.10.png [ 8.85 KiB | Viewed 2832 times ]
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Jul 2016, 01:33, edited 1 time in total.
Renamed the topic and edited the question.

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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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New post 13 Jul 2016, 18:29
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Each rectangular region has a perimeter of 2l + 2w = 30 or l + w = 15.

The whole collection of rectangles is a square, so 5w = l
You can multiply this by 2 to get 10w = 2l and substitute this into our original write up.

10w + 2w = 30 or 12w = 30, w therefore equals 2.5
5 * 2.5 = l = 12.5

12.5 * 4 = perimeter of the whole square

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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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New post 15 Jul 2016, 18:38
Call the smaller side of each rectangular b, and side of square "a".
we know that 2(a+b) = 30 and we also know that b is 1/5 of a.
so 2(a+1/5a)=30
a+1/5a = 15 (multiply both sides by 5)
6a = 80
a = 13 (approximately) then the perimeter would be 4xa = 52 (Answer D is closest)

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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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New post 21 Jul 2016, 10:58
mitko20m wrote:
Call the smaller side of each rectangular b, and side of square "a".
we know that 2(a+b) = 30 and we also know that b is 1/5 of a.
so 2(a+1/5a)=30
a+1/5a = 15 (multiply both sides by 5)
6a = 80

a = 13 (approximately) then the perimeter would be 4xa = 52 (Answer D is closest)


Answer is exact.

You miscalculated a step (in red):
\(a + \frac{a}{5} = 15\)
\(6a = 75\)
\(a = \frac{75}{6}\)
\(P = 4*a = 4*\frac{75}{6} = 50\)

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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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New post 20 Aug 2017, 13:19
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You could also simply test the answers:

Start with answer b) 146
146=4x
x=36.5 --> way too long if the perimeter of the small rectangular is 30 only

secondly, test answer d) 50
50=4x
x=12.5 --> Correct!

12.5*2=25; 2.5*2= 5 --> sums up to 30

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Re: The square region shown has been partitioned into 5 identical rectangu   [#permalink] 20 Aug 2017, 13:19
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