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Solve using a system of two equations and two unknowns.
\n" ); document.write( " A computer parts company wants to make a rectangular memory board that has
\n" ); document.write( " a perimeter of 28 centimeters and a diagonal length of 10 centimeters.
\n" ); document.write( " Find the dimensions of the board. Consider the length to be the longer side.
\n" ); document.write( ":
\n" ); document.write( "Call the two sides L & W
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\n" ); document.write( "the perimeter
\n" ); document.write( "2L + 2W = 28
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "L + W = 14
\n" ); document.write( "L = (14-W); use this form for substitution
\n" ); document.write( ":
\n" ); document.write( "The hypotenuse, (diagonal)
\n" ); document.write( "L^2 + W^2 = 10^2
\n" ); document.write( "L^2 + W^2 = 100
\n" ); document.write( ":
\n" ); document.write( "Replace L with (14-W)
\n" ); document.write( "(14-W)^2 + W^2 = 100
\n" ); document.write( ";
\n" ); document.write( "FOIL (14-W)*(14-W)
\n" ); document.write( "196 - 28W + W^2 + W^2 = 100
\n" ); document.write( "2W^2 - 28W + 196 - 100 = 0
\n" ); document.write( ":
\n" ); document.write( "A quadratic equation
\n" ); document.write( "2W^2 - 28W + 96 = 0
\n" ); document.write( ":
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "W^2 - 14W + 48 = 0
\n" ); document.write( ":
\n" ); document.write( "Factors to
\n" ); document.write( "(W-6)(W-8) = 0
\n" ); document.write( ":
\n" ); document.write( "Two solutions
\n" ); document.write( "W = 6
\n" ); document.write( "and
\n" ); document.write( "W = 8
\n" ); document.write( "Make W = 6 cm as the width, then L = 8 cm as the length
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\n" ); document.write( "Check our solution on a calc, find the hypotenuse: