100 Ft
100 Ft
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How would you make a rectangle with these objects = two 100 ft pieces of rope n only a marking pen?
You and four other students volunteer to help build a rectangular play area in a city park. Using only a marking pen and two 100-ft-long pieces of rope, describe a method in which you and your helpers can accurately stake the vertices of the rectangular play area.
If you want a square, fold each rope in half, keeping them stretched out to be most accurate, and then mark the rope at the half way point. Each rope will then be two sides of a square. This will be a square with sides equal 50 feet.
For a rectangle you can fold them again to get 1/4 lengths and mark the points. Form each rope into a square and join them. This will give you a rectangle of width 1/4 a rope (25 feet) by 1/2 a rope (50 feet). This will overlay 1/4 of each rope so the perimeter in this case will be 150 feet.
For a different rectangle, fold the ropes again to get lengths that are 1/8 the length of the rope (12.5 feet) and mark with the marking pen. You can then unfold each rope and form a rectangle that is 1/4 a rope wide and 3/4 a rope long (2/8 by 6/8). That is 25 feet by 75 feet. This uses the whole of each rope so the perimeter will be 200 feet.
You can do more folding but eventually you will reach a point where the rope will not be flexible enough to continue. What this point is I have no idea but, in principle, you could continue to do this and get just about any size rectangle you want. Best would be to subdivide the rope as many times as possible and then use these smaller measurements when forming your rectangle plus it will help to determine 90 degree angles at each corner as I describe next.
The only question remaining is how to make the corners 90 degrees. Once you have folded the rope enough times you can use a 3-4-5 right triangle. Place the one rope where you want your initial vertex and bend it so that you have at least 2 subdivisions going one way and at least 3 going the other (by these directions I mean the directions along the length and width of the rectangle you want to make). Then use the other rope to mark out 5 from the 2 point to the 3 point. When this is done you will have a 90 degree angle at the vertex. Actually you can use this method to determine directions and then use the rope to give you an area of up to 100 by 100 feet. Do one vertex and stake out the directions from this vertex to two others (mark the original point with a stake and the 2 and 3 points with a stake stretch the rope out tight guiding along these stakes and you can make whatever size you want by repeating the procedure when necessary.