document.write( "Question 200168: Hi!\r
\n" ); document.write( "\n" ); document.write( "A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure). What are the dimensions of the rectangle?\r
\n" ); document.write( "\n" ); document.write( "thank you for your help! \n" ); document.write( "
Algebra.Com's Answer #150508 by ankor@dixie-net.com(22740)\"\" \"About 
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A circular piece of sheet metal has a diameter of 20 in.
\n" ); document.write( " The edges are to be cut off to form a rectangle of area 180 in^2 (see the figure).
\n" ); document.write( "What are the dimensions of the rectangle
\n" ); document.write( ":
\n" ); document.write( "Let a = the length
\n" ); document.write( "Let b = the width
\n" ); document.write( "The diameter of 20\" = the diagonal of the rectangle
\n" ); document.write( ":
\n" ); document.write( "a^2 + b^2 = 20^2; pythag
\n" ); document.write( "a^2 + b^2 = 400
\n" ); document.write( ":
\n" ); document.write( "Area of the rectangle
\n" ); document.write( "a * b = 180; the area of the rectangle
\n" ); document.write( "b = \"180%2Fa\"
\n" ); document.write( ":
\n" ); document.write( "Substitute (180/a) in the pythag equation
\n" ); document.write( "a^2 + (\"180%2Fa\")^2 = 400
\n" ); document.write( ":
\n" ); document.write( "a^2 + \"32400%2F%28a%5E2%29\" = 400
\n" ); document.write( "Multiply equation by a^2:
\n" ); document.write( "a^4 + 32400 = 400a^2
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "a^4 - 400a^2 + 32400 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula
\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 equation a=1, b=-400, c=32400; solve for x^2
\n" ); document.write( "\"x%5E2+=+%28-%28-400%29+%2B-+sqrt%28-400%5E2+-+4+%2A+1+%2A+32400+%29%29%2F%282%2A1%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x%5E2+=+%28400+%2B-+sqrt%28160000+-+129600+%29%29%2F2+\"
\n" ); document.write( ":
\n" ); document.write( "\"x%5E2+=+%28400+%2B-+sqrt%2830400+%29%29%2F2+\"
\n" ); document.write( "Two solutions
\n" ); document.write( "\"x%5E2+=+%28400+%2B+174.346+%29%2F2+\"
\n" ); document.write( "\"x%5E2+=+574.356%2F2\"
\n" ); document.write( "x^2 = 287.178
\n" ); document.write( "x = \"sqrt%28287.178%29\"
\n" ); document.write( "x = 16.946\" the length of the rectangle (a)
\n" ); document.write( "and
\n" ); document.write( "\"x%5E2+=+%28400+-+174.346+%29%2F2+\"
\n" ); document.write( ":
\n" ); document.write( "\"x%5E2+=+225.654%2F2\"
\n" ); document.write( "x^2 = 112.827
\n" ); document.write( "x = \"sqrt%28112.827%29\"
\n" ); document.write( "x = 10.622\" the width of the rectangle (b)
\n" ); document.write( ":
\n" ); document.write( "The rectangle is: 16.946 by 10.622
\n" ); document.write( ":
\n" ); document.write( "Check this by finding the area with these values
\n" ); document.write( "16.946 * 10.622 = 180.00 sq/in
\n" ); document.write( ":
\n" ); document.write( "Find the diameter/diagonal on a calc using these values; enter:
\n" ); document.write( "d = \"sqrt%2816.946%5E2+%2B+10.622%5E2%29\"
\n" ); document.write( "d = 20.02 ~ 20\"
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