A lifeguard uses 700 m of marker buoys to rope off a rectangular swimming area in a lake. one side of the swimming area is a sandy beach.

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perimeter = 700m 700 = 2L + W  since one side is a sandy beach. 700-2L = W     Now area = L*W = L(700-2L)    domain [0,350] 700L-2L^2  distributing the L through 700-4L   taking the first derivative =4(175-L)  the only critical number here is 175 substituting 175 for L in L(700-2L) 175(700-350) 175(350) =61250 the maximum area we first started with w = 700-2L w = 700-2L=175 Dimension: p = 700' and maximum area is a sq