document.write( "Question 901870: Hi, can someone please help me with this word problem? I have been trying to figure out the answer for the past 4 days! It says the following: \"A rectangular yard is 20 feet longer than it is wide. Determine the dimensions of the yard if it measures 100 ft diagonally.
\n" ); document.write( "The equation I came up with is the following:
\n" ); document.write( "(20+2w)(2+2w)=100ft. W=width, \r
\n" ); document.write( "\n" ); document.write( "40+40w+4w+4w^2=100
\n" ); document.write( "40+44w+4w^2-100=0
\n" ); document.write( "4w^2+44w-60=0
\n" ); document.write( "2(w^2+22w+30)=0 this is as far as I got and that's prime. I know there is a real answer not just prime. I would really appreciate your help! Thank you for your time! \n" ); document.write( "
Algebra.Com's Answer #547000 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
The diagonal is the hypotenuse and the length and width are the legs .
\n" ); document.write( "(20+x)^2+x^2=100^2
\n" ); document.write( "2x^2+40 x+400 = 10000
\n" ); document.write( "2x^2+40x - 9600=0
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\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( " So lets solve \"2%2Ax%5E2%2B40%2Ax-9600=0\" ( notice \"a=2\", \"b=40\", and \"c=-9600\")
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\n" ); document.write( " \"x+=+%28-40+%2B-+sqrt%28+%2840%29%5E2-4%2A2%2A-9600+%29%29%2F%282%2A2%29\" Plug in a=2, b=40, and c=-9600
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\n" ); document.write( " \"x+=+%28-40+%2B-+sqrt%28+1600-4%2A2%2A-9600+%29%29%2F%282%2A2%29\" Square 40 to get 1600
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\n" ); document.write( " \"x+=+%28-40+%2B-+sqrt%28+1600%2B76800+%29%29%2F%282%2A2%29\" Multiply \"-4%2A-9600%2A2\" to get \"76800\"
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\n" ); document.write( " \"x+=+%28-40+%2B-+sqrt%28+78400+%29%29%2F%282%2A2%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%28-40+%2B-+280%29%2F%282%2A2%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%28-40+%2B-+280%29%2F4\" Multiply 2 and 2 to get 4
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%28-40+%2B+280%29%2F4\" or \"x+=+%28-40+-+280%29%2F4\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-40+%2B+280%29%2F4\"
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\n" ); document.write( " \"x=240%2F4\" Add the terms in the numerator
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\n" ); document.write( " \"x=60\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=60\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-40+-+280%29%2F4\"
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\n" ); document.write( " \"x=-320%2F4\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-80\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-80\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=60\" or \"x=-80\"
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\n" ); document.write( "\n" ); document.write( "We discard negative measurements
\n" ); document.write( "x = 60 y=80
\n" ); document.write( "The length is 80 the width is 60 and the diagonal is 100
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