The rectangular floor of a classroom is $30$ feet in length and $21$ feet in width. A scale drawing of the floor has a length of $10$ inches. What is the perimeter, in inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in.

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Scale drawings: word problems

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Q. The rectangular floor of a classroom is

30

feet in length and

21

feet in width. A scale drawing of the floor has a length of

10

inches. What is the perimeter, in inches, of the floor in the scale drawing?

\newline

Answer:

\square

in.

Identify Dimensions and Scale: Identify the actual dimensions of the classroom floor and the scale used in the drawing. The actual length of the classroom floor is $30$ feet, and the actual width is $21$ feet. The scale drawing has a length of $10$ inches. We need to find the scale factor to use it for finding the width in the scale drawing and then calculate the perimeter.
Calculate Scale Factor: Calculate the scale factor. $\newline$ The scale factor is the ratio of the length in the scale drawing to the actual length. Since $1$ foot is equal to $12$ inches, we first convert the actual length from feet to inches: $30$ feet $\times 12$ inches/foot $= 360$ inches. Now we can find the scale factor: $10$ inches (scale drawing length) / $360$ inches (actual length) $= 1/36$ .
Find Width in Scale Drawing: Use the scale factor to find the width in the scale drawing. $\newline$ Now we apply the scale factor to the actual width to find the width in the scale drawing. First, convert the actual width to inches: $21 \text{ feet} \times 12 \text{ inches/foot} = 252 \text{ inches}$ . Then multiply by the scale factor: $252 \text{ inches} \times (1/36) = 7 \text{ inches}$ . So, the width in the scale drawing is $7 \text{ inches}$ .
Calculate Perimeter: Calculate the perimeter of the scale drawing. $\newline$ The perimeter of a rectangle is given by the formula $P = 2(\text{length} + \text{width})$ . We have the length as $10$ inches and the width as $7$ inches in the scale drawing. So, the perimeter is $P = 2(10\,\text{inches} + 7\,\text{inches}) = 2(17\,\text{inches}) = 34\,\text{inches}$ .