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?

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

your answer would be b

step-by-step explanation:

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm