A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved. What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.
Show Hint
When dividing an area into multiple sections using ropes, consider how the ropes intersect and how the plots are separated by each additional rope.
Step 1: Analyze the problem.
The land is divided by straight ropes passing through poles. To divide the land into four sections, we need to strategically place additional ropes that divide the land into distinct plots. Each rope can pass through three poles, forming a straight line.
Step 2: Evaluate the situation.
There are already two ropes, R1 and R2, placed in the figure. To create four plots, we need to add three additional ropes that intersect the existing ropes at points where they can divide the land into four distinct sections.
Step 3: Conclusion.
Through strategic placement of three additional ropes, we can divide the land into four equal plots. Thus, the minimum number of additional ropes needed is 3.
Thus, the correct answer is (D) 3.
