Question

Jenny has 280 meters of fencing and wishes to form three sides of a rectangular field. the fourth side borders a river and will not need fencing. as shown below, one of the sides has length x (in meters). find a function that gives the area a(x) of the field in terms of x

Answer 1

L + 2w = 120
L = 120 - 2w
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A = Lw
A = (120 - 2w)w
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Area is now a quadratic function of width (w):
A(w) = -2ww + 120w + 0
A(w) = (-2)w^2 + 120w + 0
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the above quadratic equation is in standard form, with a=-2, b=120, and c=0
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to find the maximum area A(w), plug this:
-2 120 0
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Answer 1:
the maximum point of the above quadratic equation is: ( 30, 1800 )
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so the maximum area that can be enclosed is: 1800 sq.m (the y-coordinate of the maximum point)

Answer 2

Answer:

a(x) = x*y = x*(280 - 2x) square meters

Step-by-step explanation:

In the figure attached, a plot of the problem is shown. Let's call y the length of the side that parallels the river

The perimeter that the fence cover is:

2x + y =  280 meters

Isolating y:

y =  280 meters - 2x

The area of the field is:

a(x) = x*y = x*(280 - 2x) square meters