document.write( "Question 150955: Use a system of equations to solve the word problem. The perimeter of a rectangle is 56 inches, and its area is 192 square inches. What are the dimensions? \n" ); document.write( "

Algebra.Com's Answer #110911 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"A+=+192\"$ in2
\n" ); document.write( " $\"P+=+56\"$ in
\n" ); document.write( "Let $\"l\"$ = length
\n" ); document.write( "Let $\"w\"$ = width
\n" ); document.write( " $\"l%2Aw+=+192\"$
\n" ); document.write( " $\"w+=+192%2Fl\"$
\n" ); document.write( " $\"2l+%2B+2w+=+56\"$
\n" ); document.write( " $\"2l+%2B+2%2A%28192%2Fl%29+=+56\"$
\n" ); document.write( " $\"2l+%2B+384%2Fl+=+56\"$
\n" ); document.write( "multiply both sides by $\"l\"$
\n" ); document.write( " $\"2l%5E2+%2B+384+=+56l\"$
\n" ); document.write( " $\"2l%5E2+-+56l+%2B+384+=+0\"$
\n" ); document.write( "divide both sides by $\"2\"$
\n" ); document.write( " $\"l%5E2+-+28l+%2B+192+=+0\"$
\n" ); document.write( "Solve by completing the square
\n" ); document.write( " $\"l%5E2+-+28l+=+-192\"$
\n" ); document.write( " $\"l%5E2+-+28l+%2B+%2828%2F2%29%5E2+=+-192+%2B+%2828%2F2%29%5E2\"$
\n" ); document.write( " $\"l+-+14%29%5E2+=+196+-+192\"$
\n" ); document.write( " $\"l+-+14%29%5E2+=+4\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"l+-+14+=+2\"$
\n" ); document.write( " $\"l+=+16\"$
\n" ); document.write( " $\"l+-+14+=+-2\"$
\n" ); document.write( " $\"l+=+12\"$
\n" ); document.write( "I'll graph it to check
\n" ); document.write( " $\"+graph%28+700%2C+600%2C+-5%2C+20%2C+-5%2C+10%2C+x%5E2+-+28x+%2B+192%29+\"$
\n" ); document.write( "Looks like the length can be either $\"16\"$ or $\"12\"$
\n" ); document.write( "If $\"l=16\"$ ,
\n" ); document.write( " $\"l%2Aw+=+192\"$
\n" ); document.write( " $\"w+=+192%2F16\"$
\n" ); document.write( " $\"w+=+12\"$
\n" ); document.write( "The length is 16 and the width is 12 (answer)
\n" ); document.write( "If $\"l+=+12\"$
\n" ); document.write( " $\"w+=+192%2F12\"$
\n" ); document.write( " $\"w+=+16\"$ This is really the same answer with $\"w+%3El\"$
\n" ); document.write( "which it shouldn't be
\n" ); document.write( "check answer:
\n" ); document.write( " $\"2l+%2B+2w+=+56\"$
\n" ); document.write( " $\"2%2A16+%2B+2%2A12+=+56\"$
\n" ); document.write( " $\"32+%2B+24+=+56\"$
\n" ); document.write( " $\"56+=+56\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );