
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 24th, 2016, 12:21 AM  #1 
Member Joined: Aug 2016 From: South Korea Posts: 54 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: 903 Thanks: 331 
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: 7,929 Thanks: 1124 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: 14,299 Thanks: 1023 
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: 903 Thanks: 331 
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: 14,299 Thanks: 1023  
August 24th, 2016, 10:06 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,299 Thanks: 1023 
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: 7,929 Thanks: 1124 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: 14,299 Thanks: 1023 
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) 

Tags 
dimensions, rectangle 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculate coordinates of embedded rectangle on rotation of parent rectangle  cottontech  Geometry  4  March 30th, 2016 12:48 PM 
Greatest rectangle of given ratios from a fixed rectangle  givera  Geometry  4  October 17th, 2015 02:10 PM 
How to calc sides of rectangle inside a rotated rectangle  mhurkman  Algebra  4  February 7th, 2011 10:40 AM 
dimensions of a rectangle  lambic  Calculus  4  November 18th, 2009 02:51 PM 
Rectangle, finding dimensions + area, hw help  mieky9999  Algebra  4  March 14th, 2009 04:04 AM 