1. Choose a room you would like to decorate. Measure its length or width. This
measurement will be the length of your pennant string.
2. Choose a size of paper square to use. (Hint: Whole number side lengths will
make the calculations easier.)
3. Cut the square in half along the diagonal to form two paper triangles
(pennant flags).
4. Measure the length of the diagonal. Then use the Pythagorean Theorem to
find its exact length.
5. You will attach each triangle to the string along its diagonal side, with no
space between triangles. Divide the length of the string by the length of the
diagonal to determine how many triangles you will need.
6. Determine the number of triangles you will need to cover the entire length of the string by dividing the length of the string by the length of each triangle.
7. Round up the number of triangles needed to the nearest whole number to ensure you have enough triangles to cover the entire string without leaving gaps.
8. Cut out the required number of triangles from the paper square, using the diagonal as one side of each triangle.
9. Attach each triangle to the string by folding the diagonal side over the string and securing it with glue or tape. Make sure there is no space between each triangle to create a continuous pennant string.
10. Repeat steps 8 and 9 until all the triangles are attached to the string, covering the entire length of the string.
11. Hang the pennant string in your chosen room, using hooks or adhesive tabs, to decorate the space according to your preference. Adjust the string's length if necessary by adding or removing triangles.
12. Optional: Decorate the triangles with patterns, colors, or designs to personalize your pennant string and match your room's theme or style.
To determine how many triangles you will need for your pennant string, you need to follow these steps:
1. Choose a room you want to decorate and measure its length or width. Let's say the length of the room is 10 feet. This measurement will be the length of your pennant string.
2. Choose a size of paper square to use. For easier calculations, it's recommended to use whole number side lengths. Let's say you choose a paper square with a side length of 4 inches.
3. Cut the square in half along the diagonal to form two paper triangles, which will be your pennant flags.
4. Measure the length of the diagonal of one of the triangles. To do this, use a ruler or measuring tape and measure from one corner of the triangle to the opposite corner along the longest side. Let's say the diagonal measures 5 inches.
5. Use the Pythagorean Theorem to find the exact length of the diagonal. The Pythagorean Theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the diagonal, and the other two sides are the lengths of the triangle's legs.
The formula is: Diagonal^2 = Leg1^2 + Leg2^2
Let's denote the length of one leg as "a" and the length of the other leg as "b." So, a = 4 inches and b = 4 inches because the triangle is a right triangle with two congruent sides.
Plugging the values into the formula: Diagonal^2 = 4^2 + 4^2
Diagonal^2 = 16 + 16
Diagonal^2 = 32
Taking the square root of both sides, we find:
Diagonal = √32
Diagonal ≈ 5.66 inches
Therefore, the exact length of the diagonal is approximately 5.66 inches.
6. Now you need to determine how many triangles you will need to cover the entire length of your pennant string. Divide the length of the string (10 feet) by the length of the diagonal of one triangle (5.66 inches). Remember to convert the measurements to the same unit before dividing.
Since there are 12 inches in a foot, the length of the string in inches is 10 feet * 12 inches/foot = 120 inches.
Dividing the length of the string by the length of the diagonal:
Number of triangles = 120 inches / 5.66 inches
Number of triangles ≈ 21.16 triangles
Since you can't have a fraction of a triangle, you would need to round up to the nearest whole number. So, in this case, you would need 22 triangles to cover the entire length of the pennant string.
Following these steps will help you determine how many triangles you need to decorate your chosen room with a pennant string.