Choose a room you would like to decorate:

_My Bed room___________________________
Measure the length of one wall in inches: ___72_______________________

2. Choose a size of paper to use.
*I recommend just using a standard 8.5 inch by 11 inch piece of paper. Then fold it diagonally and cut it to make a square.

*Once you cut off the bottom portion of the rectangular, the sides of the square will each be 8.5 inches. If you would like, you can cut 0.5 inch off the top of the square and 0.5 off the right side of the square to make it 8 inches by 8 inches. That is optional.

3. Cut the square in half along the diagonal to form two paper triangles. These will be your pennant flags.

4. Measure the diagonal of the triangle: Use the Pythagorean Theorem ( a^2+b^2=c^2) to determine the length of the diagonal (hypotenuse):

A2 + B2 = C2
122 + 122 = 24
24 + 24 = 72

*Your actual measurement and your Pythagorean Theorem answer should be the same or very similar.

5. Divide the actual length of the room (measurement from Step 1), by the length of the hypotenuse:
72 x 4 = 288
288 / 72 = 4

*That is how many triangles you will need to create your “string of pennant flags”.
How many flags will you need to cover the entire length of the wall? 288


Analyze It Questions:
Why might your measurement of the diagonal’s length be different than the length you found using the Pythagorean Theorem?

Your measurement of the diagonal’s length might be off track, but my measurements were fine so I am on the right track.

Aaaa thankss so much this is really helpful. Btw, for the analyze question another answer may be "The Pythagorean Theorem is more precise, whilst a ruler/tape measure usually gives an estimate."

There could be several reasons why the measurement of the diagonal's length might be different than the length found using the Pythagorean Theorem.

One possible reason is human error in measuring the length of the diagonal or the length of one wall. If the measurements are not accurate, it can lead to a discrepancy between the actual length and the calculated length using the Pythagorean Theorem.

Another reason could be the presence of uneven surfaces or obstacles along the wall, which can affect the measurement of the diagonal. If there are irregularities in the wall, it can cause the diagonal to be longer or shorter than expected.

Additionally, the material used for the pennant flags, such as paper or fabric, may have some flexibility or stretch. This can slightly alter the length of the diagonal when measuring it directly compared to the calculated length using the Pythagorean Theorem.

It's important to double-check and ensure the accuracy of measurements, as well as consider any possible factors that may affect the measurement of the diagonal's length.

There can be a few reasons why your measurement of the diagonal's length may be different from the length found using the Pythagorean Theorem:

1. Measurement error: When manually measuring the diagonal of the triangle, there is always a chance of making a mistake or encountering some error in measurement. This can result in a slightly different length compared to the one calculated using the Pythagorean Theorem, which is based on the precise mathematical relationship between the sides of a right-angled triangle.

2. Rounded measurements: If you rounded your measurements during the process, especially when measuring the length of the wall or the sides of the square, it can affect the accuracy of the final result. Ideally, measurements should be as precise as possible to minimize any discrepancies.

3. Inaccurate cutting: When cutting the square in half to form two triangles, if the cut is not perfectly aligned or straight, it can slightly alter the shape of the triangles and potentially lead to variations in the diagonal length.

The Pythagorean Theorem, on the other hand, is a mathematical formula that calculates the exact relationship between the sides of a right-angled triangle. It provides a precise measure of the diagonal length based on the lengths of the other two sides. However, in practical scenarios, there can always be some small differences due to measurement and human error.