document.write( "Question 222512: If the length of a rectangle is 3 feet longer than the width and the diagonal is 5 feet, then what are the length and width? \n" ); document.write( "

Algebra.Com's Answer #166707 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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If the length of a rectangle is 3 feet longer than the width and the diagonal
\n" ); document.write( "is 5 feet, then what are the length and width?
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\n" ); document.write( "Using a^2 + b^2 = c^2
\n" ); document.write( "where
\n" ); document.write( "let x = width (a)
\n" ); document.write( "then
\n" ); document.write( "(x+3) = the length (b)
\n" ); document.write( "and
\n" ); document.write( "c = 5
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\n" ); document.write( "x^2 + (x+3)^2 = 5^2
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + x^2 + 6x + 9 = 25
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\n" ); document.write( "2x^2 + 6x = 9 - 25 = 0
\n" ); document.write( ":
\n" ); document.write( "2x^2 + 6x - 16 = 0
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "x^2 + 3x - 8 = 0
\n" ); document.write( "Use the quadratic formula to find x
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "in this problem: a=1; b=3; c=8
\n" ); document.write( " $\"x+=+%28-3+%2B-+sqrt%283%5E2+-+4+%2A1%2A-8+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( ":
\n" ); document.write( "Do the math and you should get a positive solution: x=1.7 is the width
\n" ); document.write( "and
\n" ); document.write( "4.7 is the length
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\n" ); document.write( "Check on a calc enter $\"sqrt%281.7%5E2+%2B+4.7%5E2%29\"$ = 4.998 ~ 5 \n" ); document.write( "

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