Geometry and Distance Question

Question

A perfectly straight road borders 4 farms. Each farm is identical in size and shape; that is, each farm is exactly 90 acres and in the precise shape of a semi-circle, with the flat side of each semi-circle bordering the road. The 4 farms are contiguously aligned along the road, with precisely 100 yards of open land between their borders.

How long is the total distance (in feet and in miles) from the left-most edge of the left most farm to the right-most edge of the right-most farm?

Answer 1

Draw and label a diagram.

The space between the farms totals 300 yards

1 acre = 4840 yd²

90 acre = 435600 yd² yet that is only a semi-circle

180 acre = 871200 yd²

Now for the diameter

871200 = πr²

277.31 ≈ r²

16.65 ≈ r

33.3 = d

133.22 = 4d

The distance is 300 + 133.22 yards.