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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

Best Answer 

 #1
avatar+7339 
+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
edited by hectictar  Apr 16, 2018
 #1
avatar+7339 
+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
edited by hectictar  Apr 16, 2018

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