Rectangular Playing Field

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A regulation NFL playing field of length
x and width y has a perimeter of (1040)/3 yards.

(a) Show that the width of the rectangle is y = (520/3) − x and its area is A = x[(520/3) − x].

(b) Graph A = x[(520/3) − x] on the xy-plane.

(c) From the graph in part (b), estimate the dimensions
of the rectangle that yield a maximum area.

I need steps or hints for parts (a) and (c). I can use Desmos to graph part (b).

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[+3] - engineer - 05/19/2021For part a, remember that the perimeter is length + length + width + width = x + x + y + y = 2x + 2y. For part c, look at the graph you made in part b, find the maximum area and look at the...

@nycdad,

For part a, remember that the perimeter is length + length + width + width = x + x + y + y = 2x + 2y.

For part c, look at the graph you made in part b, find the maximum area and look at the value of x that produced that maximum. From that and the equation given in part a, compute the width.

Rectangular Playing Field

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