The area X of the overlapping region (shaded more darkly) is one eighth of the total shaded area.

What fraction of the area of one rectangle is X?

Kindly provided by UKMT A rectangle is placed obliquely on top of an identical rectangle, as shown.
The area X of the overlapping region (shaded more darkly) is one eighth of the total shaded area. What fraction of the area of one rectangle is X?
7 Comments
Rodolfo
10/5/2015 01:30:16 am
Let A = area of 1 rectangle.
Reply
Simon
10/5/2015 03:21:45 am
I found the same except I used R for the area of one rectangle!
Reply
tom
18/6/2015 01:56:15 am
And I called the one rectangle area Y. So between us we have
Reply
Cgreene
10/5/2015 06:05:35 am
((A1+A2)-ax)/8=ax is where I started since A1=A2 2A1/8=9ax/8 or ax/A1=2/9. I checked by using 72 for A1 then A1+A2=144 and 2/9 72=16 144-16=128 and 128/8=16 check
Reply
10/5/2015 01:12:59 pm
I get 1/4 or 1/5 depending on how you interpret "total shaded area"
Reply
10/5/2015 01:27:13 pm
The area of the entire figure is 8X. The light-grey area of non-intersection in 7X (by subtracting the dark-grey area).
Reply
John Rowland
10/5/2015 01:33:06 pm
Yes - my error
Reply
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