"You have been asked to help build a rectangular play area at the new Tracy elementary school. You arrive at the site eager to begin! Much to your surprise, the only things available to work with are two pieces of rope.
Explain how you can use the rope to find the vertices of the rectangle. Include an illustration and a detailed explanation of your solution."
So I've been stuck on this for a while now, and i cant figure it out, I know it has something to do with properties of a parallelogram/rectangle.
The opposite sides have to be the same. That makes it a parallelogram, a good start.
Now the diagonals have to be the same. That makes it a rectangle.
Of course, bear in mind that the diagonal can't be longer than the longer of the two ropes. (Unless you can join them together)
Explain how you can use a quick picture to find 3 times 2.7.
To find the vertices of a rectangle using only two pieces of rope, you can utilize the properties of a rectangle, including the fact that opposite sides are parallel and equal in length.
Here is a step-by-step guide on how to proceed:
1. Start by selecting a point on the ground where you want one corner of the rectangle to be located. Mark this point as A.
2. Take one rope and tie it around a stake at Point A. This rope will be the length of one side of the rectangle. Keep the remaining length of the rope free.
3. Walk along the line formed by the rope until it is taut, and then mark the ground at the end point. This point will be the opposite corner of the rectangle. Label this point as B.
4. Now, move back to Point A and align the second rope along the line formed by AB.
5. Walk along the line formed by the second rope until it is taut, and then mark the ground at the end point. This point will be one of the remaining corners of the rectangle. Label this point as C.
6. Lastly, walk back to the starting point, Point A, and walk along the second rope in the opposite direction until it is taut. Mark the ground at the end point. This point will be the last corner of the rectangle. Label this point as D.
7. By connecting the marked points A, B, C, and D, you will have created a rectangular play area.
Please note that it is important to keep the ropes taut and walk along them in a straight line to ensure accurate positioning of the vertices.
Here is an illustration of the process:
```
A -------- B
| |
| |
| |
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D -------- C
```
By following this method, you can use the two pieces of rope to determine the vertices of a rectangular play area at the Tracy elementary school.