Question 35991
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.