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The length of a certain rectangle is 4 centimeters longer than its width. And the number of square in its area exceeds 7 times the number of centimeters in its width by 18. Find its dimensions
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\n" ); document.write( "Let x = the width
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\n" ); document.write( "It says,\"The length of a certain rectangle is 4 centimeters longer than its width\"
\n" ); document.write( "Therefore:
\n" ); document.write( "(x+4) = the length
\n" ); document.write( "then
\n" ); document.write( "x(x+4) = the area
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\n" ); document.write( "\"And the number of square cm, in its area, exceeds 7 times the number of centimeters in its width by 18.\"
\n" ); document.write( "x(x+4) = 7x + 18
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\n" ); document.write( "x^2 + 4x - 7x - 18 = 0; arrange as a quadratic equation;
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\n" ); document.write( "x^2 - 3x - 18 = 0
\n" ); document.write( "Easily factors to:
\n" ); document.write( "(x - 6)(x + 3) = 0
\n" ); document.write( "Positive solution is what we want here.
\n" ); document.write( "x = 6 cm is the width
\n" ); document.write( "and
\n" ); document.write( "6 + 4 = 10 cm is the length
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\n" ); document.write( "Check the solutions, in the statement:
\n" ); document.write( "\"the number of square cm in it's area exceeds 7 times the number of centimeters in its width by 18.\"
\n" ); document.write( "10 * 6 = 7(6) + 18
\n" ); document.write( "60 = 42 + 18; confirms out answer\r
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