
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 638 Thanks: 85 
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.


Tags 
express, formula, relationship 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The relationship between 1+2+3+4+... and 1/12  Karma Peny  Math  28  November 13th, 2015 07:21 PM 
Relationship between ord(a) and ord(a^k)  Awesomo  Abstract Algebra  1  June 13th, 2014 10:49 PM 
Express cos(4a) + sin(4a) using only cos(a) and sin(a)  king.oslo  Algebra  3  September 6th, 2013 12:09 PM 
Phi and Pi relationship  ScottGonzales  Algebra  0  November 26th, 2012 09:40 AM 
relationship between dS/S and d(ln(S))  dh273  Economics  2  July 1st, 2008 04:13 AM 