Shenelle has 100100100 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width www (in meters) is modeled by: a(w)=-(w-25)^2+625a(w)=−(w−25) 2 +625a, left parenthesis, w, right parenthesis, equals, minus, left parenthesis, w, minus, 25, right parenthesis, start superscript, 2, end superscript, plus, 625 what is the maximum area possible?

Answer:625 sq. m.Step-by-step explanation:The graden's area is given as :  [tex]a(w) = -(w-25)^2+625[/tex] For maximization of area,we need to put first order derivative of given equation equals to 0 i.e. a'(w) should be equal to zero.   [tex]a'(w) = -2(w-25) = 0[/tex]On Simplifying : [tex]w-25 = 0[/tex]w = 25 meters Since we are given that Shenelle has 100 meters of fencing to build a rectangular gardenThis means perimeter is equal to 100.Formula of perimeter of rectangle : [tex]2(w+l) = 100[/tex]Where l is lengthw is widthPlugging w as 25 [tex]2(25+l) = 100[/tex]Dividing 2 in both sides [tex](25+l) = 50[/tex][tex]l = 25[/tex]So, for the maximum area the length should be 25 m and width should 25 mSo, So, maximum area [tex]=Length \times Width = 25 \times 25 = 625 m^2[/tex]Hence the maximum possible area is 625 sq. m.