document.write( "Question 196561: What is formula for finding width and height of rectangle with area of 1250 sq. feet and perimeter of 150 linear feet? \n" ); document.write( "

Algebra.Com's Answer #147300 by Edwin McCravy(20086) $\"\"$ $\"About$

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What is formula for finding width and height of rectangle with area of 1250 sq. feet and perimeter of 150 linear feet?\r
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document.write( "You have to use two formulas:\r\n" );
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document.write( "Substitute 1250 for A and 150 for P\r\n" );
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document.write( "We can make the second equation simpler by dividing\r\n" );
document.write( "both sides of the second equation by 2\r\n" );
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document.write( "Solve the second equation for W by subtracting L\r\n" );
document.write( "from both sides\r\n" );
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document.write( "Substitute  for  in the\r\n" );
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document.write( "Distribute on the right:\r\n" );
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document.write( "Get 0 on the right:\r\n" );
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document.write( "Factor this by writing down all the \r\n" );
document.write( "pairs of integer factors of 1250\r\n" );
document.write( "and the sum of these two factors. Sum\r\n" );
document.write( "because there is a + before the last\r\n" );
document.write( "term. (When there is a - before the\r\n" );
document.write( "last term we us the difference)\r\n" );
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document.write( "factor pairs | sum of factor pairs\r\n" );
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document.write( " 1 x 1250    |        1251\r\n" );
document.write( " 2 x 625     |         627\r\n" );
document.write( " 5 x 250     |         255\r\n" );
document.write( "10 x 125     |         135\r\n" );
document.write( "25 x  50     |          75\r\n" );
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document.write( "Now we look at the list of sums to see\r\n" );
document.write( "if the middle coefficient's absolute\r\n" );
document.write( "value is among them.  Since the last \r\n" );
document.write( "number in the list is 75 and that is\r\n" );
document.write( "the absolute value of -75, the coefficient\r\n" );
document.write( "of L, we know the trinomial will factor,\r\n" );
document.write( "So we rewrite -75L by attaching\r\n" );
document.write( "the proper signs to 25L and 50L.  For\r\n" );
document.write( "the sum to come up -75L, we assign the\r\n" );
document.write( "signs so as to rewrite -75L as\r\n" );
document.write( "-25L - 50L.\r\n" );
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document.write( "Replace -75L by -25L - 50L\r\n" );
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document.write( "Factor only the first two terms on the left:\r\n" );
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document.write( "Now factor the last two terms on the left:\r\n" );
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document.write( "Now factor out \r\n" );
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document.write( "Set each factor = 0:\r\n" );
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document.write( ", \r\n" );
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document.write( "Now if the length is 25 feet, then we find the width\r\n" );
document.write( "by substituting 25 for L in \r\n" );
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document.write( "So the width is 50 feet.\r\n" );
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document.write( "Now if the length is 50 feet, then we find the width\r\n" );
document.write( "by substituting 50 for L in \r\n" );
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document.write( "So the width is 25 feet.\r\n" );
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document.write( "So it appears there are two solutions.  One is with the\r\n" );
document.write( "length of 25 feet and a width of 50 feet.  The other is\r\n" );
document.write( "with the length of 50 feet and the width of 25 feet.\r\n" );
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document.write( "But of course these are both the same rectangle, and it's\r\n" );
document.write( "just a matter of which dimension you label \"length\" and which\r\n" );
document.write( "you label \"width\".  So actually there is just one solution.\r\n" );
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document.write( "Edwin

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