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 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: 954 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 = (3-1)B [The length of a rectangle is one less than thrice its width] Substituting A from (2) into (1) we have: (3-1)B x B =420 2 x B x B =420 B x B =210 B = 14.49 A = (3-1)B = 28.98 Therefore the dimensions are 14.49 x 28.98 to 2 decimal places Thanks from SlayedByMath
 August 24th, 2016, 02:54 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond $ab=420,\quad a=3b-1$ $a=\dfrac{3\cdot420}{a}-1$ $a^2+a-1260=0\implies a=35,b=12$ Thanks from SlayedByMath
 August 24th, 2016, 06:16 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 I prefer: w = width, 3w-1 = length w(3w-1) = 420 3w^2 - w - 420 = 0 w = 12 Thanks from greg1313
 August 24th, 2016, 06:50 AM #5 Senior Member   Joined: Apr 2014 From: UK Posts: 954 Thanks: 342 I submit that the question was worded badly
August 24th, 2016, 09:06 AM   #6
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

Quote:
 Originally Posted by weirddave I submit that the question was worded badly
...so should be easier for you, being "weird"dave

 August 24th, 2016, 10:06 AM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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 Thanks from greg1313
 August 24th, 2016, 11:38 AM #8 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 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: 1038 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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### 420cm² by what length and width?

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