Lenny Conundrum #178

[matchbow]

I didn't find a thread for this, even though it's been out for a few days now.

Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) has three fields. One field is an equilateral triangle, one field is a circle, and one field is a square. The square field is 75% larger in area than the triangular field, and 50% larger in area than the circular field. In order to completely fence all three of the fields, exactly 4000 metres of fencing is required.

What is the total area of all three fields, in square metres? Please round to the nearest whole number, and please submit the answer as just a number. For example, if the answer is 150 square metres, you would just submit the number "150".

It's just pure math. very annoying math, but totally doable. if you use a whole lot of decimals and a good calculator, it shouldn't be a problem

[AySz88]

I messed up somewhere while trying to just use pencil and paper and calculator. I ended up just using Goal Seek in Excel, which still needs some tedious equation manipulation....

But that half-hour shall not go to waste! I can say for certain that 8500/(2+2/sqrt(7) * 3^(3/4) + sqrt(2/3*pi)) is NOT the answer.

[edit] Sum of digits in my answer = 34

[miz sparrow]

Answer: 334888 square meters