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August 24th, 2016, 12:21 AM  #1 
Member Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0  What are the dimensions of the given rectangle?
The area of a rectangle is 420 cm². The length of a rectangle is one less than thrice its width. What are the dimensions of the given rectangle?

August 24th, 2016, 02:46 AM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
Let A be the length and B be the width of the rectangle 1) A x B = 420 [The area of a rectangle is 420 cm²] 2) A = (31)B [The length of a rectangle is one less than thrice its width] Substituting A from (2) into (1) we have: (31)B x B =420 2 x B x B =420 B x B =210 B = 14.49 A = (31)B = 28.98 Therefore the dimensions are 14.49 x 28.98 to 2 decimal places 
August 24th, 2016, 02:54 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond 
$ab=420,\quad a=3b1$ $a=\dfrac{3\cdot420}{a}1$ $a^2+a1260=0\implies a=35,b=12$ 
August 24th, 2016, 06:16 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
I prefer: w = width, 3w1 = length w(3w1) = 420 3w^2  w  420 = 0 w = 12 
August 24th, 2016, 06:50 AM  #5 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
I submit that the question was worded badly 
August 24th, 2016, 09:06 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  
August 24th, 2016, 10:06 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
On a timed test, use short cuts if possible; like: when is 3w^2 >= 420 ? try 10: 3w^2 = 300 try 11: 3w^2 = 363 try 12: 3w^2 = 432 ....ahhhh, so: Apply the "1": 12 * 3  1 = 35 12 * 35 = 420 
August 24th, 2016, 11:38 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond 
I submit that I shouldn't do math before morning coffee! 
August 24th, 2016, 04:27 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
With me, not before at least 2 coffees: the one for my left eye, followed by the one for my right eye! (extra large, Tim Horton's dark roast brand) 

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