Answer: 17 rolls
Explanation:
First, we need to find the total length of crepe paper needed to go around the perimeter of the ceiling. To do this, we can multiply the length of each side by the number of sides:
length of crepe paper = length of each side x number of sides
The ceiling of Frank's living room is a square, so it has four sides. Plugging in the given values, we get:
length of crepe paper = 20 ft x 4
Performing the calculation gives us:
length of crepe paper = 80 ft
Next, we need to find the length of crepe paper needed to go from each corner of the ceiling to the opposite corner. To do this, we can use the Pythagorean theorem to find the length of the diagonal of the ceiling:
diagonal length = sqrt(length^2 + width^2)
Plugging in the given values, we get:
diagonal length = sqrt(20^2 + 20^2)
Performing the calculation gives us:
diagonal length = 28.28 ft
Since there are four corners in the ceiling, we will need 4 x 28.28 ft of crepe paper to go from each corner to the opposite corner. This is a total of 113.12 ft of crepe paper.
To find the total length of crepe paper needed, we can add the length needed for the perimeter and the length needed for the corners:
total length = perimeter length + corner length
Plugging in the values we calculated above, we get:
total length = 80 ft + 113.12 ft
Performing the calculation gives us:
total length = 193.12 ft
Finally, we can divide the total length of crepe paper needed by the length of each roll to find out how many rolls Frank needs to buy:
number of rolls = total length / length of each roll
Plugging in the given values, we get:
number of rolls = 193.12 ft / 12 ft
Performing the calculation gives us:
number of rolls = 16.09 rolls
Since Frank can only buy whole rolls of crepe paper, he will need to buy 17 rolls to decorate