I originally was presented with this conundrum as a challenge on a website, but the time limit has passed to present an answer. Still, I am not sure how to solve the conundrum.

The Farmer has 3 fields. One field is an equilateral triangle. One field is a circle. One field is a square. The square field is 75% larger in area than the triangular field. The square field is 50% larger in area than the circular field. In order to completely fence all three fields exactly 4000 meters of fencing is required. What is the total area of all three fields?

This is presented to me as a conundrum. I have worked the problem thus far:

a= circle area

x= triangle area

n= square area

n=x+(.75x)

n=a+(.5a)

or n=1.75x=1.5a

2 times Pi times the radius is a circle's circumference

4 times the length of a side is a square's perimeter

3 times the length of a side is an equilateral triangle's perimeter

Pi times the radius of the circle squared is the circle's area

The length of the side of the square squared is the square's area

Base times Height of a triangle is the triangle's area

I am sort of fuzzy about how to find the height of the equilateral triangle, but I suspect I need to know the Pythagorean theorem, which I don't remember from college.

My equation to find all the perimeter's is:

r is circular field radius

s is measure of side of square field

t is measure of side of triangular field

4000=(2*Pi*r)+(4s)+(3t)

Thank you for your help.

PS: I already posted this on an algebra tutor website, but I got an answer that seems wrong, since the person who answered it tried to solve the equation for the perimeter using the area equation variables.

"a= circle area

x= triangle area

n= square area

so n=1.75*x=1.75x

n=1.5*a=1.5a

and x+a+n=4000

x+a+1.75x=4000

a+2.75x=4000

a=4000-2.75x

x+a+1.5a=4000

2.5a+x=4000

2.5*(4000-2.75x)+x=4000

10000-6.875x+x=4000

6.875x-x=10000-4000

5.875x=6000

x=1021.28

and thus

a=4000-2.75x

a=4000-(2.75*1021.28)

a=4000-2808.51

a=1191.49

and check this out

n=1.5a=1.5*1191.49=1787.23 (let pick this one b'coz it makes 4000 even)

n=1.75x=1.75*1021.28=1787.24

x+a+n=4000

1021.28+1191.49+1787.23=4000 "

This was the tutor's answer.

Thanks for your help.