document.write( "Question 153085: The lenght of a rectangle is 6 more feet than twice the width. If the perimeter is 24 ft., what are the dimensions? \n" ); document.write( "

Algebra.Com's Answer #112570 by Electrified_Levi(103) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi, Hope I can help,
\n" ); document.write( ".
\n" ); document.write( "The length of a rectangle is 6 more feet than twice the width. If the perimeter is 24 ft., what are the dimensions?
\n" ); document.write( ".
\n" ); document.write( "First, we have to find out the variables, The length of a rectangle is 6 more feet than twice the width. If the perimeter is 24 ft., what are the dimensions?
\n" ); document.write( ".
\n" ); document.write( "We see that the width is \"x\", the length is 6 more feet than twice the width, or \"2x + 6\", now we will place the variables into a formula
\n" ); document.write( ".
\n" ); document.write( "the Perimeter formula for a rectangle = $\"+2%28length%29+%2B+2%28width%29+=+Perimeter+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+2%28L%29+%2B+2%28W%29+=+Perimeter+\"$
\n" ); document.write( ".
\n" ); document.write( "We can replace the width and length into the formula, our Perimeter = 24 feet
\n" ); document.write( ".
\n" ); document.write( " $\"+2%28L%29+%2B+2%28W%29+=+Perimeter+\"$ = $\"+2%282x+%2B+6%29+%2B+2%28x%29+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( "We will use distribution
\n" ); document.write( ".
\n" ); document.write( " $\"+2%282x+%2B+6%29+%2B+2%28x%29+=+24+\"$ = $\"+4x+%2B+12+%2B+2x+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( "We will add like terms
\n" ); document.write( ".
\n" ); document.write( " $\"+4x+%2B+12+%2B+2x+=+24+\"$ = $\"+4x+%2B+2x+%2B+12+=+24+\"$ = $\"+6x+%2B+12+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( "We will move the \"12\" over to the right side
\n" ); document.write( ".
\n" ); document.write( " $\"+6x+%2B+12+-+12+=+24+-+12+\"$ = $\"+6x+=+12+\"$
\n" ); document.write( ".
\n" ); document.write( "We will divide each side by \"6\"
\n" ); document.write( ".
\n" ); document.write( " $\"+6x%2F6+=+12%2F6+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( ".
\n" ); document.write( "x = 2
\n" ); document.write( ".
\n" ); document.write( "We now know the width, since the width = \"x\"
\n" ); document.write( ".
\n" ); document.write( "width = \"x\", or \"2\"
\n" ); document.write( "length = (2x+6), or (2(2) + 6), or (4+6), or \"10\"
\n" ); document.write( ".
\n" ); document.write( "width = \"2\" feet
\n" ); document.write( "length = \"10\" feet
\n" ); document.write( ".
\n" ); document.write( "\"10\" is 6 more feet than twice the width(2)
\n" ); document.write( ".
\n" ); document.write( "We can check by replacing \"x\" in our equation ( x = 2)
\n" ); document.write( ".
\n" ); document.write( " $\"+2%282x+%2B+6%29+%2B+2%28x%29+=+24+\"$ = $\"+2%282%282%29+%2B+6%29+%2B+2%282%29+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+2%282%282%29+%2B+6%29+%2B+2%282%29+=+24+\"$ = $\"+2%284+%2B+6%29+%2B+2%282%29+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+2%284+%2B+6%29+%2B+2%282%29+=+24+\"$ = $\"+2%2810%29+%2B+2%282%29+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+2%2810%29+%2B+2%282%29+=+24+\"$ = $\"+20+%2B+4+=+24+\"$
\n" ); document.write( ".
\n" ); document.write( " $\"+20+%2B+4+=+24+\"$ = $\"+24+=+24+\"$ (True)
\n" ); document.write( ".
\n" ); document.write( "Length = 10 feet
\n" ); document.write( "Width = 2 feet
\n" ); document.write( ".
\n" ); document.write( "Hope I helped, Levi \n" ); document.write( "

\n" );