document.write( "Question 912065: the perimeter of a rectangle and a square is 80 cm each. if the difference between their areas is 100 cm find the sides of the rectangle. \n" ); document.write( "
Algebra.Com's Answer #553649 by JulietG(1812)\"\" \"About 
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If the perimeter of the square is 80, then each side is 80/4, or 20.
\n" ); document.write( "That makes the area of the square 20*20=400
\n" ); document.write( "Since the difference between the rectangle and the square are is 100, the area of the rectangle equals either 500 or 300.
\n" ); document.write( "They're even numbers, so we'll assume that the sides are even, too.
\n" ); document.write( "2L + 2W = 80, therefore L + W = 40
\n" ); document.write( "We're looking for factors of 500 (or 300; we'll do that next if 500 doesn't work) that equal 40 when added.
\n" ); document.write( "Factors of 500:
\n" ); document.write( "1 and 500 = 501
\n" ); document.write( "2 and 250 =252
\n" ); document.write( "4 and 125 = 129
\n" ); document.write( "5 and 100 = 105
\n" ); document.write( "10 and 50 = 60
\n" ); document.write( "20 and 25 = 45
\n" ); document.write( "None of the factors of 500 fit the scenario. Let's try the other possibility, 300
\n" ); document.write( "Factors of 300:
\n" ); document.write( "1 and 300 = 301
\n" ); document.write( "2 and 150 = 152
\n" ); document.write( "3 and 100 = 103
\n" ); document.write( "4 and 75 = 79
\n" ); document.write( "5 and 60 = 65
\n" ); document.write( "6 and 50 = 56
\n" ); document.write( "10 and 30 = 40 -- we have a winner!
\n" ); document.write( "12 and 25 = 37
\n" ); document.write( "15 and 20 = 35
\n" ); document.write( "I'm sure there are other ways to solve this, but elimination works best for me. If you need a different way of doing it, please repost with that instruction. \n" ); document.write( "
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