Answer:
5 rolls.
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given the square ceiling has side lengths of 15√2 feet, and the side lengths of a square are equal, the perimeter of the ceiling is:
[tex]\implies 4 \times 15\sqrt{2}=60\sqrt{2}\;\; \sf ft[/tex]
Diagonal of a square
[tex]d=\sqrt{2s^2}[/tex]
where s is the side length.
Therefore, the length of the diagonal of the ceiling is:
[tex]\implies d=\sqrt{2(15\sqrt{2})^2}[/tex]
[tex]\implies d=\sqrt{2\cdot 450}[/tex]
[tex]\implies d=\sqrt{900}[/tex]
[tex]\implies d=30\;\; \sf ft[/tex]
Therefore, the total amount of crepe paper Victoria needs is:
[tex]\begin{aligned}\implies \sf Total\;length&=\sf Perimeter+2\;diagonals\\&=60\sqrt{2}+30+30\\&=144.8528137...\;\; \sf ft\end{aligned}[/tex]
If each roll contains 30 ft, to calculate the minimum number of rolls Victoria should buy, divide the total amount of crepe paper by 30 and round up to the nearest whole number:
[tex]\implies \dfrac{144.8528137...}{30}=4.828427125...[/tex]
Therefore, Victoria should buy a minimum of 5 rolls of crepe paper.
