document.write( "Question 1126355: A farmer has 70 meters of fencing and would like to use the fencing to create a rectangular garden where one of the sides of the garden is against the side of a barn.
\n" ); document.write( "Let l represent the varying length of the rectangular garden (in meters) and let A
\n" ); document.write( "represent the area of the rectangular garden (in square meters).
\n" ); document.write( "A)Write a formula that expresses A in terms of l.
\n" ); document.write( "B)What is the maximum area of the garden?
\n" ); document.write( "C)What is the length and width of the garden configuration that produces the maximum area?
\n" ); document.write( "D)What if the farmer instead had 300 meters of fencing to create the garden. What is the length and width of the garden configuration that produces the maximum area?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #742688 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A farmer has 70 meters of fencing and would like to use the fencing to create a rectangular garden where one of the sides of the garden is against the side of a barn.
\n" ); document.write( " Let L represent the varying length of the rectangular garden (in meters) and
\n" ); document.write( " let A represent the area of the rectangular garden (in square meters).
\n" ); document.write( ":
\n" ); document.write( "let w = the width of the garden
\n" ); document.write( "then three fenced sides
\n" ); document.write( "L + 2w = 70
\n" ); document.write( "2w = -L + 70
\n" ); document.write( "w = -.5L + 35
\n" ); document.write( ":
\n" ); document.write( "A)Write a formula that expresses A in terms of L.
\n" ); document.write( " A(L) = L(-.5L+35)
\n" ); document.write( " A(L) = -.5L^2 + 35L
\n" ); document.write( ":
\n" ); document.write( "B)What is the maximum area of the garden?
\n" ); document.write( "find the axis of symmetry of equation: A = -.5L^2 + 35L
\n" ); document.write( "L = \"%28-35%29%2F%282%2A-.5%29\"
\n" ); document.write( "L = +35 meters
\n" ); document.write( "A = -.5(35^2) + 35(35)
\n" ); document.write( "A = 612.5 sq/m
\n" ); document.write( ":
\n" ); document.write( "C)What is the length and width of the garden configuration that produces the maximum area?
\n" ); document.write( "L = 35 m is the length
\n" ); document.write( "w = -.5(35) + 35
\n" ); document.write( "w = 17.5 m is the width
\n" ); document.write( ":
\n" ); document.write( "D)What if the farmer instead had 300 meters of fencing to create the garden. What is the length and width of the garden configuration that produces the maximum area?
\n" ); document.write( "L + 2w = 300
\n" ); document.write( "2w = -L + 300
\n" ); document.write( "w = -.5L + 150
\n" ); document.write( ":
\n" ); document.write( "A)Write a formula that expresses A in terms of l.
\n" ); document.write( " A(L) = L(-.5L+150)
\n" ); document.write( " A(L) = -.5L^2 + 150L
\n" ); document.write( ":
\n" ); document.write( "B)What is the maximum area of the garden?
\n" ); document.write( "find the axis of symmetry of equation: A = -.5L^2 + 150L
\n" ); document.write( "L = \"%28-150%29%2F%282%2A-.5%29\"
\n" ); document.write( "L = 150 meters is the length
\n" ); document.write( "then
\n" ); document.write( "A = -.5(150^2) + 35(150)
\n" ); document.write( "A = 11,250 sq/m
\n" ); document.write( ":
\n" ); document.write( "w = -.5(150) + 150
\n" ); document.write( "w = 75 m is the width \n" ); document.write( "
\n" );