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
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document.write( "A) find an expression for the area of the square
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document.write( "B) an expression for the area of the rectangle
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document.write( "C) the lengths of the two parts of the sum of the areas is a minimum \n" );
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Algebra.Com's Answer #740144 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! 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. \n" ); document.write( ": \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) = \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( " \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 = \n" ); document.write( "find the area in terms of x, (A = \n" ); document.write( "A(x) = \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) = \n" ); document.write( "the easiest way to find the minimum area is to graph it, y = the area \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " |