Solve.A rectangular animal pen is constructed such that the length and width of have a sum of 80 feet. (i) Show that the area of the rectanglular animal pen, y, can be represented by x(80 - x), where x is the length of the rectangle. (ii) Graph the equation y = x(80 - x). (iii) What dimensions give the maximum area for the animal pen?
What will be an ideal response?
(i) If the length of the rectangle is x, and the sum of the length and width is 80, the width
can be found by solving x + w = 80 for w. This gives w = 80 - x. Using the formula for
the area of a rectangle, y = lw, the area can be represented by y = x(80 - x).
(ii) 
(iii) Length 40 and width 40
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