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.

Please Help Me!!! These are my last three questions on my homework and i dont understand them!!!

Thank You!!!!

KennedyPape
Apr 15, 2018

#1**+2 **

Katie wants to hang crepe paper on the 4 sides of the square and on the 2 diagonals.

side length of the square = 15 ft

diagonal length of square = \(\sqrt{15^2+15^2}\) ft

diagonal length of square = \(\sqrt{2\cdot15^2}\) ft

diagonal length of square = \(\sqrt2\cdot\sqrt{15^2}\) ft

diagonal length of square = \(15\sqrt2\) ft

Assuming that none of the crepe paper will hang down at all, that it will be flat against the ceiling....

length of crepe paper needed = 4( side length of square ) + 2( diagonal length of square )

length of crepe paper needed = 4( 15 ft ) + 2( 15√2 ft )

length of crepe paper needed = 60 ft + 30√2 ft

length of crepe paper needed ≈ 102.426 ft

20 ft = 1 roll

1 ft = 1/20 roll

102.426 ft = 102.426/20 rolls

102.426 ft ≈ 5.121 rolls

So she needs to buy 5.121 rolls of paper. But since she probably can't buy a fraction of a roll, and she probably wants the paper to hang down some, she needs to buy at least 6 rolls.

* edited to correct an error!!! *

hectictar
Apr 16, 2018

#1**+2 **

Best Answer

Katie wants to hang crepe paper on the 4 sides of the square and on the 2 diagonals.

side length of the square = 15 ft

diagonal length of square = \(\sqrt{15^2+15^2}\) ft

diagonal length of square = \(\sqrt{2\cdot15^2}\) ft

diagonal length of square = \(\sqrt2\cdot\sqrt{15^2}\) ft

diagonal length of square = \(15\sqrt2\) ft

Assuming that none of the crepe paper will hang down at all, that it will be flat against the ceiling....

length of crepe paper needed = 4( side length of square ) + 2( diagonal length of square )

length of crepe paper needed = 4( 15 ft ) + 2( 15√2 ft )

length of crepe paper needed = 60 ft + 30√2 ft

length of crepe paper needed ≈ 102.426 ft

20 ft = 1 roll

1 ft = 1/20 roll

102.426 ft = 102.426/20 rolls

102.426 ft ≈ 5.121 rolls

So she needs to buy 5.121 rolls of paper. But since she probably can't buy a fraction of a roll, and she probably wants the paper to hang down some, she needs to buy at least 6 rolls.

* edited to correct an error!!! *

hectictar
Apr 16, 2018