SOLUTION: 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.

Question 49079: 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

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:

Thank you for your help. By the way, I have been placed under a time limit of Wednesday night to achieve the answer.
Answer by my_math_ace(1) (Show Source): You can put this solution on YOUR website!
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
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