Problem

1986 AJHSME Problem 18

A rectangular grazing area is to be fenced off on three sides using part of a 100 meter rock wall as the fourth side. Fence posts are to be placed every 12 meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area 36 m by 60 m?

[asy] draw((0,0)--(16,12)); draw((16/3,4)--(32/3,8)--(20/3,40/3)--(4/3,28/3)--cycle); draw((16/3 +.4,4+.3)--(16/3 +.1,4+.7)--(16/3-.3,4+.4)); draw((32/3 -.3,8+.4)--(32/3 -.7,8+.1)--(32/3-.4,8-.3)); draw((20/3 -.4,40/3-.3)--(20/3 -.1,40/3-.7)--(20/3+.3,40/3-.4)); draw((4/3 +.3,28/3-.4)--(4/3 +.7,28/3-.1)--(4/3+.4,28/3+.3)); label("WALL",(7,4),SE); [/asy]

\text{(A)}\ 11 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 16

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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