document.write( "Question 1122945: An aluminum brace used to support a wooden shelf has a length that is 1 inches more than twice the width of the shelf. The brace is anchored to the wall h inches below the shelf. Find the width of the shelf and the length of the brace. (Assume h = 15.) \n" ); document.write( "
Algebra.Com's Answer #739133 by ankor@dixie-net.com(22740)\"\" \"About 
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An aluminum brace used to support a wooden shelf has a length that is 1 inches more than twice the width of the shelf.
\n" ); document.write( " The brace is anchored to the wall h inches below the shelf.
\n" ); document.write( " Find the width of the shelf and the length of the brace. (Assume h = 15.)
\n" ); document.write( ":
\n" ); document.write( "draw this out, a right triangle
\n" ); document.write( "let w = the width of the shelf
\n" ); document.write( "then (2w+1) = the length of the brace (the hypotenuse)
\n" ); document.write( "\"w%5E2+%2B+15%5E2+=+%282w%2B1%29%5E2\"
\n" ); document.write( "w^2 + 225 = 4w^2 + 4w + 1
\n" ); document.write( "combine like terms to form a quadratic equation on the right
\n" ); document.write( "0 = 4w^2 - w^2 + 4w + 1 - 225
\n" ); document.write( "3w^2 + 4w -224 = 0
\n" ); document.write( "use the quadratic equation a=3; b=4; c=-224, but this will factor to
\n" ); document.write( "(3w+28)(w-8) = 0
\n" ); document.write( "the positive solution is all we want here
\n" ); document.write( "w = 8 inches is the width of the shelf
\n" ); document.write( "then
\n" ); document.write( "2(8) + 1 = 17 inches is the length of the brace
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check on your calc: 8^2 + 15^2 = 17^2
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