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Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is $12$ feet long, and each strand of his Christmas lights will wrap around a $70$ -inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing? $\newline$ A) $6$ $\newline$ B) $7$ $\newline$ C) $8$ $\newline$ D) $9$

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Write equations of cosine functions using properties

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Q. Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

A)

6

\newline

B)

7

\newline

C)

8

\newline

D)

9

Calculate total length: Calculate the total length of the railing around three sides of the square porch. $\newline$ Since one side of the porch is $12$ feet long, the total length of the railing around three sides is $3$ times the length of one side. $\newline$ Total length $= 3 \times 12$ feet $\newline$ Total length $= 36$ feet
Convert to inches: Convert the total length from feet to inches. $\newline$ There are $12$ inches in a foot, so to convert feet to inches, we multiply by $12$ . $\newline$ Total length in inches = $36$ feet $\times 12$ inches/foot $\newline$ Total length in inches = $432$ inches
Determine strands needed: Determine how many strands of lights are needed. $\newline$ Each strand covers $70$ inches of the railing. To find out how many strands are needed, divide the total length of the railing in inches by the length that one strand covers. $\newline$ Number of strands $= \frac{\text{Total length in inches}}{\text{Length one strand covers}}$ $\newline$ Number of strands $= \frac{432\,\text{inches}}{70\,\text{inches}}$ $\newline$ Number of strands $= 6.1714\ldots$
Round up to whole number: Round up to the nearest whole number since Kris cannot use a fraction of a strand. $\newline$ Kris needs at least $7$ strands because you cannot have a fraction of a strand and he needs to cover the entire railing.

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