document.write( "Question 1207752: A pond is enclosed by a wooden deck that is 3 feet wide.The fence surrounding the deck is 100 feet long. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(a) If the pond is square, what are its dimensions? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(c) If the pond is circular, what is its diameter? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(d) Which pond has the most area? \n" ); document.write( "

Algebra.Com's Answer #845801 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.\r
\n" ); document.write( "\n" ); document.write( "(a) If the pond is square, what are its dimensions?\r
\n" ); document.write( "\n" ); document.write( "(b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?\r
\n" ); document.write( "\n" ); document.write( "(c) If the pond is circular, what is its diameter?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  If the pond is a square, then the fence is a square, too,\r\n" );
document.write( "\r\n" );
document.write( "     and the side length of the fenced square is, OBVIOUSLY,  100/4 = 25 feet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Then the side of the pond itself is  25 - 3 - 3 = 19 feet.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "     (we subtract 3 feet from each side).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  Let x be the shorter dimension of the pond, in feet.\r\n" );
document.write( "\r\n" );
document.write( "     Then the longer dimension of the pond is 3x feet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     The dimensions of the fence are (x+6) feet by (3x+6) feet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     The perimeter of the fence is 2(x+6) + 2(3x+6) = 2x + 12 + 6x + 12 = 8x + 24  feet.\r\n" );
document.write( "\r\n" );
document.write( "     We equate it to 100 feet\r\n" );
document.write( "\r\n" );
document.write( "           8x + 24 = 100\r\n" );
document.write( "\r\n" );
document.write( "     and find x:  x =  =  = 9.5 feet.\r\n" );
document.write( "\r\n" );
document.write( "     The dimensions of the pond itself are 9.5 feet and 9.5*3 = 28.5 feet.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     CHECK  for the perimeter of the fence  2*(9.5+6) + 2*(28.5+6) = 2*15.5 + 2*34.5 = 31 + 69 = 100 feet.  ! correct !\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  First find the diameter of the fenced circle\r\n" );
document.write( "\r\n" );
document.write( "           D =  =  = 31.831 feet  (rounded).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Next, find the diameter of the pond itself\r\n" );
document.write( "\r\n" );
document.write( "           d = 31.831 - 2*3 = 25.831  feet  (rounded).    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(d)   The squared pond (a) has the area  19*19 = 361 sq. feet.\r\n" );
document.write( "\r\n" );
document.write( "      The rectangular pond (b) has the area  9.5*28.5 = 270.75 sq. feet.\r\n" );
document.write( "\r\n" );
document.write( "      The circular pond (c) has the area   =  = 524.049 sq. feet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      The greatest area is for circular pond (c).    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved in full, with complete explanations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );