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 #768935 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Tutor @ikleyn shows a clever way of solving a problem like this. Two numbers add to 50 and have a product of 456; so call the two numbers 25+x and 25-x and solve the equation

\n" ); document.write( " $\"%2825%2Bx%29%2825-x%29+=+456\"$

\n" ); document.write( "That is a nice shortcut, because the product on the left is 625-x^2, making it relatively easy to solve the problem.

\n" ); document.write( "For many students, it will be even faster simply to solve the basic problem by trial and error: find two numbers whose sum is 50 and whose product is 456.

\n" ); document.write( "There are many pairs of integers whose sum is 50 and far fewer pairs of integers whose product is 456. So look for a pair of integers with a product of 456 that has a sum of 50.

\n" ); document.write( "456*1 obviously not
\n" ); document.write( "228*2
\n" ); document.write( "152*3
\n" ); document.write( "114*4
\n" ); document.write( "76*6
\n" ); document.write( "57*8
\n" ); document.write( "38*12 AHA! That's it! \n" ); document.write( "

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