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Four ( $4 \times 7$) rectangles are removed from the corners of a square having side length ($8n + 1$), as shown in the Figure. Determine the largest integer $n $ for which the perimeter of Figure  is less than $1000$.

 

 Feb 3, 2021
 #1
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The removal of the rectangles  does  not affect the  perimeter.......the firgure has exactly the same  perimeter as that  of the  square

 

So

 

4 (8n + 1)   <  1000

 

32n +  4  <  1000

 

32n  <  996

 

n  <  996   /  32  

 

n <  31 + 1/8

 

So    n  =   31

 

 

cool cool cool

 Feb 3, 2021

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