document.write( "Question 316286: If the length of a rectangle is four times it's width and the area is 256ft squared then what is the perimeter? \n" ); document.write( "
Algebra.Com's Answer #226204 by Shogun(3)![]() ![]() ![]() You can put this solution on YOUR website! First things first: Let's jot down everything we know about the problem, to make it easier. \r \n" ); document.write( "\n" ); document.write( "Area of a Rectange: Length * Width\r \n" ); document.write( "\n" ); document.write( "Perimeter of a Rectangle: 2*Length + 2*Width\r \n" ); document.write( "\n" ); document.write( "Now we know that the LENGTH of the rectangle is 4 TIMES its WIDTH.\r \n" ); document.write( "\n" ); document.write( "So let's call the width \"W\". Then we can say that the length is 4W (since length is 4 times the width). \r \n" ); document.write( "\n" ); document.write( "Now that we know both length and width, we can make a formula (from our area equation).\r \n" ); document.write( "\n" ); document.write( "256 = 4W * W. <--- All we did here is substitute numbers back into the equation.\r \n" ); document.write( "\n" ); document.write( "We can simplify that to get:\r \n" ); document.write( "\n" ); document.write( "256 = 4W^2\r \n" ); document.write( "\n" ); document.write( "64 = W^2\r \n" ); document.write( "\n" ); document.write( "8 = W\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So now we know that the width is 8 from our formula. That means we also know that the length is 32 (4 times the width, which is 8).\r \n" ); document.write( "\n" ); document.write( "The final step is to find the perimeter, which we know is 2*Length + 2*Width.\r \n" ); document.write( "\n" ); document.write( "2*32 + 2*8 = 64 + 16 = 80.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So we know that the perimeter is 80 ft. \r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |