SOLUTION: Please help 4)Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of

Question 35991: Please help

4)Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.
Answer:
Show work in this space.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
LET LENGTH BE L AND WIDTH BE W
WE HAVE PERIMETER =2(L+W)=300
L+W=150
W=150-L.............................I
AREA =LW=L(150-L)= - (L^2-150L) = - {(L^2-2*L*75+75^2)-75^2}
= 75^2 - (L-75)^2.......SINCE (L-75)^2 IS ALWAYS POSITIVE ,AND IT IS
TO BE SUBTRACTED FROM 75^2 TO GET THE AREA,WE GET MAXIMUM AREA WHEN
THIS IS MINIMUM...OR...L-75=0....OR....L=75
SO FOR MAXIMUM AREA THE PATIO SHOULD BE A SQUARE OF 75' LENGTH AND 75' WIDTH.
RELATED QUESTIONS
Please help! Submitted question earlier didn't get a response. 4) Amanda has 400 feet (answered by venugopalramana,Prithwis)

Again please help. 4) Amanda has 400 feet of lumber to frame a rectangular patio (the... (answered by Paul)

Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle... (answered by Paul)

Hi, please help me with this word problem. Amanda has 400 feet of lumber to frame a... (answered by checkley75)

Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle... (answered by mbarugel)

Hello, I would like to know if I did this problem correctly. Can you help me, please?... (answered by 303795)

Can anyone help me with this doozy? Amanda has 400 feet of lumber to frame a... (answered by stanbon)

4) Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a... (answered by checkley71)

Having trouble understanding this! 4) Amanda has 400 feet of lumber to frame a... (answered by checkley71)