Subjects algebra

Fence Posts 5Bbe86

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1. **Problem statement:** We have a rectangular grazing area measuring 36 m by 60 m. One side of length 60 m is along a rock wall, so it does not need fencing. The other three sides (two sides of 36 m and one side of 60 m) need fencing with posts placed every 12 meters, including posts at the corners where the fence meets the wall. 2. **Identify the sides to be fenced:** - Two sides of length 36 m each - One side of length 60 m 3. **Calculate the number of posts on each side:** Posts are placed every 12 meters, including posts at both ends. Number of posts on a side of length $L$ is given by: $$\text{posts} = \frac{L}{12} + 1$$ 4. **Calculate posts on each side:** - For each 36 m side: $$\frac{36}{12} + 1 = 3 + 1 = 4$$ posts - For the 60 m side: $$\frac{60}{12} + 1 = 5 + 1 = 6$$ posts 5. **Total posts if counted separately:** $$4 + 4 + 6 = 14$$ posts 6. **Adjust for shared corner posts:** The two 36 m sides and the 60 m side meet at corners, so corner posts are counted twice in the sum above. There are 2 corners where the 36 m sides meet the 60 m side, so we subtract 2 posts to avoid double counting: $$14 - 2 = 12$$ posts 7. **Final answer:** The minimum number of posts required is **12**. **Answer: B 12**