MATH SOLVE

9 months ago

Q:
# Farmer Ed has 2,500 meters of fencing,and wants to enclose a rectangular plotthat borders on a river. If Farmer Eddoes not fence the side along the river,what is the largest area that can beenclosed?The largest area that can be enclosed

Accepted Solution

A:

Answer:Because it is a rectangle, the area is expressed as A = xy, or length times width.
Because it is next to the river, he only needs to fence three sides, so F = x + 2y.
Knowing the amount of fencing available is 7500m, we get:
7500 = x + 2y solve for x
x = 7500 - 2y substitute into the area equation
A = (7500 - 2y)y distribute
A = -2y2 +7500y
You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875
x = 7500 - 2(1875) = 3750
A = 3750(1875) = 7,031,250 m2Step-by-step explanation: