document.write( "Question 117871: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal
\n" ); document.write( "of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
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Algebra.Com's Answer #85933 by ankor@dixie-net.com(22740)\"\" \"About 
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The length of a rectangle is 1 cm longer than its width. If the diagonal
\n" ); document.write( "of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
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\n" ); document.write( "Let x = the width
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\n" ); document.write( "(x+1) = the length
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\n" ); document.write( "The sides and the diagonal from a right triangle so we can use pythagorus here
\n" ); document.write( "a^2 + b^2 = c^2
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\n" ); document.write( "In our problem a = x; b = (x+1); c = 4
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\n" ); document.write( "x^2 + (x+1)^2 = 4^2
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\n" ); document.write( "FOIL (x+1)(x+1)
\n" ); document.write( "x^2 + x^2 + 2x + 1 = 16
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\n" ); document.write( "2x^2 + 2x + 1 - 16 = 0
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\n" ); document.write( "2x^2 + 2x - 15 = 0; a quadratic equation
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\n" ); document.write( "Solve for x using the quadratic formula; a=2; b=2; c=-15
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
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\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+2%5E2+-+4+%2A+2%2A+-15+%29%29%2F%282%2A2%29+\"
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\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%284+-+%28-120%29+%29%29%2F%284%29+\"
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\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28124+%29%29%2F%284%29+\"; minus a minus is a plus
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\n" ); document.write( "\"x+=+%28-2+%2B+11.1355%29%2F4\"; we only want the positive solution here
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\n" ); document.write( "\"x+=+9.1355%2F4\"
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\n" ); document.write( "x = 2.284 cm is the width
\n" ); document.write( "then
\n" ); document.write( "2.284 + 1 = 3.284 cm is the length
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\n" ); document.write( "Check our solution:
\n" ); document.write( "2.284^2 + 3.284^2 =
\n" ); document.write( " 5.2 + 10. 8 = 16 which is 4^2 \n" ); document.write( "
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