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The square region shown has been partitioned into 5 identical rectangu

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HarveyKlaus
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The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  Updated on: 14 Jul 2016, 01:33
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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

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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.
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] 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] 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] New post  15 Jul 2016, 18:38
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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] New post  21 Jul 2016, 10:58
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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] New post  10 Jul 2019, 21:54
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I think that a lot of people, such as myself, have issues with this question because they miss the "square region shown" statement at the beginning of the stem, allowing someone to make the deductions necessary to solve this.
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  22 Dec 2019, 19:57
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in the event someone is still having trouble like me...

the question directly states that that picture is a square

We can deduce a few things

x= width
y= length

1) 2x+2y = 30 (from the prompt)
2) 5x = Y (because the picture is a square all sides are equal)

Using substitution -

2(x+y)=30
2(6x)=30
X=2.5

if x=2.5 then one side is equal to 5*(2.5) = 12.5

There are 4 sides so 4*12.5 = 50
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  19 Dec 2020, 16:26
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2(l+w) = 30
l + w = 15

Since the figure is a square we can conclude 5w = l

6w = 15
w = 2.5

5w = 12.5

12.5 * 4 sides = 50

Answer is D.
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  12 Jun 2021, 19:25
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HarveyKlaus wrote:

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

Show Spoiler
Attachment:
Screen Shot 2016-07-14 at 02.25.10.png


Each rectangle has a length:width:perimeter ratio of 5:1:12.
To get the perimeter of the square, we can add up the perimeters of the five rectangles, and subtract the four internal lengths twice (each of those internal lengths is counted twice as we add up the rectangles, and we don't want to count them at all).
Since the length of each rectangle is 5/12 of its perimeter (see the ratio above), we must subtract 5/12 of 30, a total of eight times.
\(8*(5/12)*30 = (10/3)*30 = 100\)
Therefore, the square's perimeter is:
\(5*30 - 100 = 50\)
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The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  26 Jul 2021, 13:15
HarveyKlaus wrote:

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

Show Spoiler
Attachment:
The attachment Screen Shot 2016-07-14 at 02.25.10.png is no longer available


Based off of the stem let's assume the following about respective sides of the square and 5 identical rectangular regions. So this means that we're looking for the value of 10X + 2Y. Let's lay out some equations:

(1) 5X=Y because 5 sides of the given rectangle must be equal to one length of the given rectangle.
(2) 2X+2Y = 30 -> X+Y=15

So now let's use equation (1) to simplify the value we're looking for. If 5X=Y then that means we just need to find 10X + 2(5Y), or 20X. So if we can find the value of X then we can answer this question.

Alright well if X+Y = 15 then X+5X = 15, and then X = 15/6.

So 20(15/6) = 50.
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  27 Jun 2022, 02:25
HarveyKlaus wrote:

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

Show Spoiler
Attachment:
Screen Shot 2016-07-14 at 02.25.10.png


Given, 2(L+W)=30
=> L+W=15-----------------(1)

We want to know the perimeter of the square:
Perimeter of square= 4*W or (10L+2W) or (5L+W)*2

*In a square all 4 sides are equal,

Therefore, 5L=W

Plugging this into (1):
=> L+5L=15
=>L=2.5; W=12.5

Perimeter of Square= 4*w = 4*12.5 = 50.00

P.s:
*When I took the actual practice test, I panicked and tried to solve the question without using that fact.
Was there anyone else who missed that too?
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink] New post  23 Jul 2023, 23:50
Let side of square be 5a,

As per given condition, 2(5a+a)=30
=>a=2.5

Perimeter of square=4*5a=20a=50

Hence D
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Re: The square region shown has been partitioned into 5 identical rectangu [#permalink]
23 Jul 2023, 23:50
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