document.write( "Question 99525: the area of square field is 5184 m. square. a rectangular field , whose length is twice its breadth has its perimeter equal to the perimeter of the square field . find the area of the rectangular field. \n" ); document.write( "
Algebra.Com's Answer #72388 by doukungfoo(195)\"\" \"About 
You can put this solution on YOUR website!
First lets look at the square field. We are given that its area equals 5184 m.
\n" ); document.write( "Lets find its perimeter. We know that the area of a square is equal to its length times its width. or \"%28L%29%28W%29=5184\" because it is a square we know that its length and width are equal so to find them all we have to do is take the square root of 5184. so \"sqrt%285184%29=72\"
\n" ); document.write( "Now we know that each side of the square field is 72 meters.
\n" ); document.write( "The perimeter of a square is equal to the sum of all its sides.
\n" ); document.write( "Since there are four sides to a square, all we have to do to find the perimeter is multiply 4 times 72. Ok well \"%284%29%2872%29=288\"
\n" ); document.write( "So the perimeter of the square field is 288 meters.
\n" ); document.write( "Now lets take a look at the rectangle field.
\n" ); document.write( "Lets use L and W to describe its length (L) and its width (W)
\n" ); document.write( "We are told that its length is twice its breadth (or width)
\n" ); document.write( "lets write that as an equation
\n" ); document.write( "\"L=2W\"
\n" ); document.write( "Thats length equals two times width.
\n" ); document.write( "We are also told that its perimeter is equal to the perimeter of the square field. And we know that the square field perimeter is 288 meters.
\n" ); document.write( "The perimeter of a rectangle is equal to the sum of all its sides.
\n" ); document.write( "since there are two sides that represent the length and two sides that represent the width we can express the perimeter of the rectangle field with this equation:
\n" ); document.write( "\"%282L%29%2B%282W%29=288\"
\n" ); document.write( "Now because we are told that \"L=2W\"
\n" ); document.write( "we can replace the L in \"%282L%29%2B%282W%29=72\" with 2W like this:
\n" ); document.write( "\"%282%282W%29%29%2B%282W%29=288\"
\n" ); document.write( "Now we can solve for W
\n" ); document.write( "\"%282%282W%29%29%2B%282W%29=288\"
\n" ); document.write( "\"%284W%29%2B%282W%29=288\"
\n" ); document.write( "\"6W=288\"
\n" ); document.write( "\"W=48\"
\n" ); document.write( "Ok so the width of the rectangle field is 48 meters.
\n" ); document.write( "We can now use this to find the length.
\n" ); document.write( "\"%282L%29%2B%282W%29=288\"
\n" ); document.write( "\"%282L%29%2B%282%2848%29%29=288\"
\n" ); document.write( "\"%282L%29%2B%2896%29=288\"
\n" ); document.write( "\"%282L%29=288-96\"
\n" ); document.write( "\"%282L%29=192\"
\n" ); document.write( "\"L=96\"
\n" ); document.write( "Finally we have found the length of the rectangle field to be 96 meters
\n" ); document.write( "and the width to be 48 meters. To find the area of this field all that is left
\n" ); document.write( "to do is multiply its length (96) times is width (48) so
\n" ); document.write( "\"%2896%29%2848%29=4608+m%5E2\"\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );