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In the figure shown, two rectangular regions overlap to form

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Asif123
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In the figure shown, two rectangular regions overlap to form [#permalink] New post   08 Feb 2020, 08:39
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In the figure shown, two rectangular regions overlap to form a triangular region, which is shaded.
The perimeters of the rectangles are 15 and 21, and the perimeter of the triangle is 6.

Quantity A
Quantity B
The sum of the lengths of the thick line segments
30




A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


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#greprepclub In the figure shown, two rectangular regions overlap to form a triangular region.jpg
#greprepclub In the figure shown, two rectangular regions overlap to form a triangular region.jpg [ 13.71 KiB | Viewed 12014 times ]
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C
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Re: In the figure shown, two rectangular regions overlap to form [#permalink] New post   18 Jul 2020, 11:45
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Asif123 wrote:
Image

In the figure shown, two rectangular regions overlap to form a triangular region, which is shaded.
The perimeters of the rectangles are 15 and 21, and the perimeter of the triangle is 6.

Quantity A
Quantity B
The sum of the lengths of the thick line segments
30




Show: ::
Attachment:
#greprepclub In the figure shown, two rectangular regions overlap to form a triangular region.jpg


NOTE: Let's say the top rectangle has perimeter 21, which means the bottom rectangle has perimeter 15

Let's first examine the top (blue) rectangle.
Let c = of the length of the portion of the blue rectangle that is NOT part of the thick line segments
Image
Since the top (blue) rectangle has perimeter 21, we know that the total length of the blue thick line segments = 21 - c


Now let's examine the bottom (red) rectangle.
Let a and b = the lengths of the portion of the blue rectangle that is NOT part of the thick line segments
Image
Since the bottom (red) rectangle has perimeter 15, we know that the total length of the red thick line segments = 15 - a - b



Combine everything to get:
Image


The sum of the lengths of the thick line segments = (21 - c) + (15 - a - b)
= 36 - a - b - c
= 36 - (a + b + c)
= 36 - 6 [ since we're told the perimeter of the shaded triangle is 6]
= 30

Answer: C

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Re: In the figure shown, two rectangular regions overlap to form [#permalink] New post   08 Feb 2020, 11:17
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The sum of perimeters of the two rectangular regions less the perimeter of the triangle. We can show it this way.

Let's denote the base of the triangular as x.

Since the base of the triangle also includes a part of the sum of the perimeters of rectangular, the sum of the lengths of the thick line segments equals to:

15 + 21 - x - (6 - x) = 15+21 - 6 = 30.

The answer is C.
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Re: In the figure shown, two rectangular regions overlap to form [#permalink] New post   12 Jun 2020, 19:01
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Expert Reply
Asif123 wrote:
Image

In the figure shown, two rectangular regions overlap to form a triangular region, which is shaded.
The perimeters of the rectangles are 15 and 21, and the perimeter of the triangle is 6.

Quantity A
Quantity B
The sum of the lengths of the thick line segments
30




A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


Show: ::
Attachment:
#greprepclub In the figure shown, two rectangular regions overlap to form a triangular region.jpg


This is one of those questions that looks difficult, but is really pretty straightforward with a bit of creative thinking.

Imagine pulling that lower rectangle all the way down, so that it is completely outside the upper rectangle, and just touches it at a single point. Then, the total perimeter would be 36: the sum of the perimeters of the two rectangles.

Once you move the lower rectangle back up inside the upper rectangle, those three lines that make up the triangle are no longer part of the perimeter of the figure, so we can simply subtract the triangle.

Since we know the perimeter of the triangle is 6, it's simply 36 - 6 = 30.

Answer: C
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Re: In the figure shown, two rectangular regions overlap to form [#permalink] New post   13 Jun 2024, 08:21
Hello from the GRE Prep Club BumpBot!

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Re: In the figure shown, two rectangular regions overlap to form [#permalink]
13 Jun 2024, 08:21
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