Question

Farmer ed has 450 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. if farmer ed does not fence the side along the​ river, find the length and width of the plot that will maximize the area. what is the largest area that can be​ enclosed?

Answer 1

Let

x--------> the length of the plot (side along the​ river)

y--------> the width of the plot

we know that

Area of the plot=x*y------> equation 1

perimeter of the plot=x+2y

perimeter of the plot=450 m

so

x+2y=450-----> 2y=450-x------> divide by 2 both sides

y=225-0.50x-------> equation 2

substitute the equation 2 in equation 1

A=x*[225-0.50x]------> A=225x-0.50x²

using a graph tool

see the attached figure

the vertex is the point (225, 25312.5)

that means for x=225 m the value of the area is a maxim

find the value of y

A=x*y-------> y=A/x-----> y=25312.5/225------> y=112.5 m

the answer part a) is

the length of the plot (side along the​ river) is 225 m

the width of the plot is 112.5 m

the answer part b) is

the largest area that can be​ enclosed is 25,312.5 m²