document.write( "Question 1082006: The top of a kitchen island is a piece of granite that has an area of 15ft^2. It is 3.5 ft longer than it is wide. Find the dimensions of the surface. \n" ); document.write( "
Algebra.Com's Answer #696147 by Theo(13342)\"\" \"About 
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length * width = area.
\n" ); document.write( "let L = length and W = width and you get:
\n" ); document.write( "L * W = area
\n" ); document.write( "since area = 15, you get:
\n" ); document.write( "L * W = 15
\n" ); document.write( "since L = W + 3.5, you get:
\n" ); document.write( "(W + 3.5) * W = 15
\n" ); document.write( "simplify to get W^2 + 3.5W = 15
\n" ); document.write( "subtract 15 from both sides of the equation to get:
\n" ); document.write( "W^2 + 3.5W - 15 = 0
\n" ); document.write( "multiply both sides of this equation by 2 to get:
\n" ); document.write( "2W^2 + 7W - 30 = 0
\n" ); document.write( "factor this equation to get:
\n" ); document.write( "(2W - 5) * (W + 6) = 0
\n" ); document.write( "W can be either 5/2 or -6
\n" ); document.write( "since it can't be minus, then it has to be 5/2.
\n" ); document.write( "when W = 5/2, L = W + 3.5 becomes L = 5/2 + 7/2 = 12/2
\n" ); document.write( "L * W becomes 5/2 * 12/2 = 60/4 = 15
\n" ); document.write( "solution looks good.
\n" ); document.write( "if you can't factor the quadratic equation, then use the quadratic formula.
\n" ); document.write( "you will get the same answer.
\n" ); document.write( "the graph of W^2 + 3.5W - 15 = y and the graph of 2W^2 + 7W - 30 = y look like this.
\n" ); document.write( "as you can see, the roots of both equations are the same, even though the equations are different.
\n" ); document.write( "they have the same values only when y = 0.
\n" ); document.write( "\"$$$\"\r
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