My Math Forum Finding the width of a uniform border

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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: 2,766 Thanks: 4 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: $$$W-2B$$$$H-2B$$=\frac{3WH}{4}$ $WH-2BW-2BH+4B^2=\frac{3WH}{4}$ $4B^2-2(W+H)B+\frac{WH}{4}=0$ $16B^2-8(W+H)B+WH=0$ Application of the quadratic formula yields: $B=\frac{8(W+H)\pm\sqrt{64(W+H)^2-64WH}}{32}=\frac{W+H\pm\sqrt{W^2+H^2+WH}}{4}$ Letting W = 15 m and H = 12 m, we find: $B\approx0.89,12.61$ The only root that makes sense is $B\approx0.89$
 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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# a mural is to be painted on a wall 12x15. if the mural is to cover 75% of the area, how wide must the border be

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