The ceiling of Katie's living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.

The perimeter of a square is p=4s and we wish to know how many 20ft rolls of crepe paper are needed to equal this perimeter or more ...

20n≥4s we know s=15ft so

20n≥60 upon division by 20 of both sides ...

n≥3

So the minimum would be 3 rolls.

I think that 3 rolls is wrong and that 6 rolls is right. If you create a 15 by 15 square and draw two lines through the center that connect to the opposite corner, you'll be able to use the Pythagorean Theorem.

Perimeter: 15+15+15+15=60ft.

Length of Line from Corner to Corner:

(15) (15) + (15) (15) = C^2

225+225=C^2

450=C^2

21.2=C

21.2 (2) = 42.4ft.

42.4ft.+60ft. = 102.4ft.

102.4ft. divided by 20ft. = 5.12 = 6 rolls