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A square is divided into five rectangles, and all the rectangles have the same area. Given that AB = 1, find the side length of the square.

 

 Aug 3, 2022
 #1
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Already answered by BuilderBoi, further down in the thread.

 Aug 3, 2022
 #2
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See https://web2.0calc.com/questions/geometry_363

 Aug 3, 2022
 #3
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BuilderBoi  already found the area to be 25/9

 

So the side of the square =  sqrt (25/9)  = 5/3

 

Here's the proof

 

The  top of the  square  has the length   5/9 + 5/9 + 5/9 =  15/9 =  5/3

 

By symmetry  the   top edge of one of the two rectangles at the bottom = (5/3) (1/2) =  5/6

 

And the area of one of these rectangles =  5/9

 

So  the other dimension  of one of these rectangles must be  (5/9) / (5/6) = 6/9 =  2/3

 

And AB =  1

 

So....the  side of the  square is also   1 + 2/3   =  5/3

 

 

 

 

cool cool cool

 Aug 3, 2022

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