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

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Manager
Joined: 18 Feb 2015
Posts: 86
The square region shown has been partitioned into 5 identical rectangu [#permalink]

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Updated on: 14 Jul 2016, 01:33
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

69% (01:40) correct 31% (01:45) wrong based on 204 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

Attachment:

Screen Shot 2016-07-14 at 02.25.10.png [ 8.85 KiB | Viewed 4795 times ]

Originally posted by HarveyKlaus on 13 Jul 2016, 17:29.
Last edited by Bunuel on 14 Jul 2016, 01:33, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 02 Jun 2016
Posts: 40
Schools: Sloan '19 (II)
Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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13 Jul 2016, 18:29
3
2
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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Intern
Joined: 18 Jan 2012
Posts: 39
Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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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)
Intern
Joined: 08 Mar 2016
Posts: 13
Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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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)

You miscalculated a step (in red):
$$a + \frac{a}{5} = 15$$
$$6a = 75$$
$$a = \frac{75}{6}$$
$$P = 4*a = 4*\frac{75}{6} = 50$$
Intern
Joined: 22 Apr 2017
Posts: 5
Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]

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20 Aug 2017, 13:19
1
You could also simply test the answers:

146=4x
x=36.5 --> way too long if the perimeter of the small rectangular is 30 only

50=4x
x=12.5 --> Correct!

12.5*2=25; 2.5*2= 5 --> sums up to 30
Re: The square region shown has been partitioned into 5 identical rectangu   [#permalink] 20 Aug 2017, 13:19
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