document.write( "Question 71427: the length of a rectangle is 3 times the width. If the width were increased by 4 and the length remains the same the resulting rectangle would have an area of 231 sq.inches. find the dimension of the original. \n" ); document.write( "
Algebra.Com's Answer #51179 by ankor@dixie-net.com(22740)\"\" \"About 
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The length of a rectangle is 3 times the width. If the width were increased by 4 and the length remains the same the resulting rectangle would have an area of 231 sq.inches. find the dimension of the original.
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\n" ); document.write( "The dimensions of the original:
\n" ); document.write( "Let x = width
\n" ); document.write( "Then 3x = length
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\n" ); document.write( "Dimensions of the larger rectangle:
\n" ); document.write( "(x+4) = width, (original width increased by 4)
\n" ); document.write( "3x = length, (remains the same)
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\n" ); document.write( "Area of larger:
\n" ); document.write( "3x(x+4) = 3x^2 + 12x
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\n" ); document.write( "\"resulting rectangle would have an area of 231\"
\n" ); document.write( "3x^2 + 12x = 231
\n" ); document.write( "3x^2 + 12x - 231 = 0; our old friend, the quadratic equation
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\n" ); document.write( "Simplify, divide equation by 3:
\n" ); document.write( "x^2 + 4x - 77 = 0
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\n" ); document.write( "Easily factors to:
\n" ); document.write( "(x+11)(x-7) = 0
\n" ); document.write( "x = +7, the solution we want here
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\n" ); document.write( "Original rectangle: 7 by 3(7);
\n" ); document.write( "21 by 7 ft
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\n" ); document.write( "Check: using the area of 231:
\n" ); document.write( "21 * (7+4) = 231\r
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