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November 1st, 2011, 01:26 PM  #1 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Finding the width of a uniform border
A mural is to be painted on a wall that is 15 units long and 12 units high. A border of uniform width is to surround the mural. If the mural is to cover 75% of the area of the wall, how wide must the border be?

November 1st, 2011, 01:32 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5  Re: Finding the width of a uniform border
The "75%..." part is the easiest to tackle. The wall has area 12 x 15 = 180 (square units), so we want our mural to have area .75*180 = 135 (square units). Now we determine the dimensions of the mural. The requirement of a "uniform border" means that the mural will have dimensions (15  2x)*(12  2x), where x is the width of the border. ^ deducing this is often the hardest part of problems like this, so draw a picture and see why my claim is true. So (15  2x)*(12  2x) = 135 is the equation for the area of the mural. FOIL, get in standard form, then factor/quadratic formula. 
November 1st, 2011, 01:33 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Finding the width of a uniform border
Let W be the width and H be the height of the wall, and B be the width of the border. We then require: Application of the quadratic formula yields: Letting W = 15 m and H = 12 m, we find: The only root that makes sense is 
November 1st, 2011, 03:57 PM  #4 
Newbie Joined: Nov 2011 Posts: 1 Thanks: 0  Re: Finding the width of a uniform border
ZOMG you don't know? so nooby


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