document.write( "Question 1147573: A playground has an area of 456 meters and a perimeter of 100 meters. How long and wide is it? \n" ); document.write( "

Algebra.Com's Answer #768917 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A playground has an area of 456 $\"highlight%28square%29\"$ meters and a perimeter of 100 meters. How long and wide is it?
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\n" ); document.write( "\n" ); document.write( "Traditional way to solve it is THIS :\r
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document.write( "    Let W be the width.  \r\n" );
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document.write( "    Then the length is   = 50-W.\r\n" );
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document.write( "    The area is  \r\n" );
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document.write( "        W*(50-W) = 456.\r\n" );
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document.write( "    and you need to solve this quadratic equation, which I leave to you.\r\n" );
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\n" ); document.write( "This way is traditional and boring.\r
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\n" ); document.write( "\n" ); document.write( "I will show you now another way, unexpected, fresh and elegant.\r
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document.write( "    The sum of the width and the length is 50.\r\n" );
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document.write( "    Consider the value of  = 25, which is the average of the length and the width.\r\n" );
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document.write( "    It is equally remoted from the length and the width :  \r\n" );
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document.write( "        25 = W + x = L - x     (1)\r\n" );
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document.write( "    where \"x\" is some value, unknown to you now.\r\n" );
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document.write( "    From (1),  W = 25-x,  L = 25+x  and the area = L*W = (25+x)*(25-x) =  - ,\r\n" );
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document.write( "    so you have this equation\r\n" );
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document.write( "        625 - x^2 = 456.\r\n" );
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document.write( "    Then  x^2 = 625 - 456 = 169,  so  x =  = 13.\r\n" );
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document.write( "    ANSWER.  The length of the rectangle is 25+13 = 38 meters.  The width of the rectangle is  25-13 = 12 meters.\r\n" );
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document.write( "    CHECK.   38*12 = 456 square meters.   ! Correct !\r\n" );
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document.write( "It is the way to solve such problems mentally, without using equations.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle\r
\n" ); document.write( "\n" ); document.write( "    - Three methods to find the dimensions of a rectangle when its perimeter and the area are given\r
\n" ); document.write( "\n" ); document.write( "    - Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Dimensions and the area of rectangles and circles and their elements\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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