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The numbers inside the rectangles represent the area of these rectangles. What is the area of the green rectangle?

 

 May 28, 2020
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Let  a  be the length across the top of the red rectangle.

Let  b  be the length across the top of the blue rectangle.

Let  c  be the height across the left side of the red rectangle.

Let  d  be the height across the left side of the yellow rectangle.

 

Therefore, the area of the

   red rectangle is:      a·c  =  12

   blue rectangle is:     b·c  =  15

   yellow rectangle is:  a·d  =  8

   green rectangle is:  b·d  =  ??

 

a·c  =  12   --->   a  =  12/c

a·d  =  8     --->   a  =  8/d

Combining these two equations:  12/c  =  8/d   --->   12d  =  8c   --->   3d  =  2c   --->   c  =  3d/2

 

  b·c  =  15   --->   c  =  15/b

 

Combining  c  =  15/b  with  c  =  3d/2   --->   15/b  =  3d/2   --->   3bd  =  30   --->   b·d  =  10

 May 28, 2020

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