Enigma 1393: More haste less seed
10 September 2013
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From New Scientist #2553, 27th May 2006
I designed a water feature for my garden, fenced in for safety. I planned to buy three pieces of fencing to form a triangular boundary, with two of them being equal in length. Then I planned to make the biggest possible circular pool within the triangle, seeding the rest of the area with grass.
In my haste at the garden centre I bought the two correct equal-length pieces, but the third piece was only three-quarters as long as it should have been. I constructed a triangle with the incorrect fencing and made the largest circular pond possible within it.
It turned out that the area enclosed by the triangle was exactly the same as I had intended in my original plan but, surprisingly, the radius of the pool I ended up with was one foot greater than I had originally planned. What three lengths of fencing did I actually buy?