document.write( "Question 1123737: A piece of wire 6 metres long is cut into two parts, one of which is used to form a square and the other to form a rectangle whose length is three times its width. If x is the length of the wire used to form the square
\n" ); document.write( "A) find an expression for the area of the square
\n" ); document.write( "B) an expression for the area of the rectangle
\n" ); document.write( "C) the lengths of the two parts of the sum of the areas is a minimum
\n" ); document.write( "

Algebra.Com's Answer #740144 by ankor@dixie-net.com(22740)\"\" \"About 
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A piece of wire 6 metres long is cut into two parts, one of which is used to form a square and the other to form a rectangle whose length is three times its width.
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\n" ); document.write( " If x is the length of the wire used to form the square:
\n" ); document.write( "then
\n" ); document.write( "(6-x) = the length to form the rectangle
\n" ); document.write( ":
\n" ); document.write( "A) find an expression for the area of the square.
\n" ); document.write( "A(x) = \"%28x%2F4%29%5E2\"
\n" ); document.write( "B) an expression for the area of the rectangle
\n" ); document.write( "let w = the width of the rectangle
\n" ); document.write( "then
\n" ); document.write( "3w = the width
\n" ); document.write( "and
\n" ); document.write( "\"3w%5E2\" = the area
\n" ); document.write( "the relationship of w to (6-x); the perimeter of the rectangle
\n" ); document.write( "2w + 6w = (6-x)
\n" ); document.write( "8w = (6-x)
\n" ); document.write( "w = \"%286-x%29%2F8\"
\n" ); document.write( "find the area in terms of x, (A = \"3w%5E2\") replace with x
\n" ); document.write( "A(x) = \"3%28%286-x%29%2F8%29%5E2\" is the area of the rectangle
\n" ); document.write( ":
\n" ); document.write( "C) the lengths of the two parts of the sum of the areas is a minimum
\n" ); document.write( "A(x) = \"%28x%2F4%29%5E2\" + \"3%28%286-x%29%2F8%29%5E2\"
\n" ); document.write( "the easiest way to find the minimum area is to graph it, y = the area
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\n" ); document.write( "minimum area when x = 2.5 m the length to form the square
\n" ); document.write( "and
\n" ); document.write( "6 - 2.5 = 3.5 m the length to form the rectangle
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