MATH SOLVE

3 months ago

Q:
# A rectangular area is to be fenced in with 300 feet of chicken wire. find the maximum area that can be enclosed.

Accepted Solution

A:

Let the lengths of the sides of the rectangle be x and y. Then A(Area) = xy and 2(x+y)=300. You can use substitution to make one equation that gives A in terms of either x or y instead of both.

2(x+y) = 300

x+y = 150

y = 150-x

A=x(150-x) <--(substitution)

The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:

0=x(150-x)

x=0, 150

So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.

A=75(150-75)

A=75*75

A=5625

So the maximum area that can be enclosed is 5625 square feet.

2(x+y) = 300

x+y = 150

y = 150-x

A=x(150-x) <--(substitution)

The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:

0=x(150-x)

x=0, 150

So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.

A=75(150-75)

A=75*75

A=5625

So the maximum area that can be enclosed is 5625 square feet.