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February 20th, 2016, 09:17 PM  #1 
Newbie Joined: Feb 2016 From: Singapore Posts: 1 Thanks: 0  Can you express this relationship as a formula?
Today we were given a challenging Math Investigation in school and I require extra assistance from you. I was wondering what the relationship between the arrangement of 12 squares join together and how the perimeter differs for each arrangement. For the number of squares given, the perimeter would change depending on each arrangement. The exact question we were given is as follows: Can you see how the perimeter has been affected by how you arrange the slabs? Can you express this relationship as a formula? Also, when arranging the 12 (1 x 1m) squares, the squares cannot be overlapped nor can they connected only from the conners. Also, no holes in between the arrangements. Examples are included. Thank you! 
February 21st, 2016, 06:11 PM  #2 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 561 Thanks: 79 
If the 12 slabs are next to each other in a 1x12 or 12x1 rectangle, the perimeter will be 12 + 1 + 12 + 1 = 26. If the 12 slabs are in a 3x4 or 4x3 rectangle, the perimeter will be 3 + 4 + 3 + 4 = 14. The smallest possible perimeter with an area of 12 is a square with a perimeter of about 13.8564 (8*square root of 3), but with 12 slabs that cannot be cut, you can't make a square. The range of possible perimeters is 14 to 26.


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