The square region shown has been partitioned into 5 identical rectangu

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):
\(a + \frac{a}{5} = 15\)
\(6a = 75\)
\(a = \frac{75}{6}\)
\(P = 4*a = 4*\frac{75}{6} = 50\)

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.

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

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.

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:
\(5*30 - 100 = 50\)

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.

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?

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