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by anshulseth » Wed May 06, 2009 12:37 am
6. In the figure above, two rectangles with the same dimensions overlap to form the shaded region. If each rectangle has perimeter 12 and the shaded region has perimeter 3, what is the total length of the heavy line segments?
(A) 15 (B) 18 (C) 21
(D) 22 (E) 23

Refer to the attached figure.

Please explain the working
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by bluementor » Wed May 06, 2009 4:55 am
I'm assuming the heavy length segments are the outer shape of the diagram.

Have a look at the attached diagram.

let say the perimeter of the overlap (which is a triangle) = a + b + c = 3.

when both rectangles (rectangle 1 on the left, and rectangle 2 on the right) do not overlap, their respective perimeters are 12 and 12.

when they overlap, part of the perimeter of rectangle 1 is 'lost'. This lost section is c. the same way, part of perimeter of rectangle 2 is lost. This lost section of rectangle 2 is a+b.

So the perimeter of the diagram = (12 - c) + (12 - b - a)
= 24 - a - b - c
= 24 - (a + b + c)
= 24 - 3
= 21

Choose C.

-BM-
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by anshulseth » Wed May 06, 2009 8:54 am
OA is C

I liked ur approach, BM
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by bluementor » Thu May 07, 2009 12:45 am
:)

-BM-
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