A rectangular piece of land to be developed as a memorial park has an area of 75 m^2. The length of the lot is three times the width of the lot. A rectangular path whose width is x meters is to be constructed along the inner perimeter of the lot. The land contained within the landscape the inner field is $3.00 per square meter. express the total cost to develop this lot as a function of x, the width of the path.

Let length = lwidth = wlength = 3 times width = 3wArea of the land = 75 sq. mArea = length × width = 3w×w = 753w²=75w²=25w=5 mlength = 3×15 = 15mNow lets make the figure with the path of width x meters(Refer the attached figure for easy understanding)The inner length is the length of the rectangle reduced by x meters on either side due to the path that is 15-x-x = 15-2xthe inner width is the width reduced by x meters in either side = 5-x-x = 5-2xNow lets calculate the inner area = inner length × inner width(15-2x)×(5-2x)= [tex] 75-30x-10x+4x^{2} [/tex]= [tex] 75-40x+4x^{2} [/tex] sq. mNow the function to calculate the cost f(x) is given by $3.00 × area of the inner landf(x) = 3 × {75-40x+4x²)= 225-120x+12x²or = 12x²-120x+225