The rectangular floor of a classroom is $30$ feet in length and $24$ feet in width. A scale drawing of the floor has a length of $10$ inches. What is the area, in square inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in. $^{2}$

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Q. The rectangular floor of a classroom is

30

feet in length and

24

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

10

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

\newline

Answer:

\square

in.

^{2}

Determine Scale Factor: First, we need to determine the scale factor between the actual floor and the scale drawing. We do this by dividing the length of the floor in the scale drawing by the actual length of the floor. $\newline$ Scale factor $= \frac{\text{Length of scale drawing}}{\text{Actual length of floor}}$ $\newline$ Scale factor $= \frac{10 \text{ inches}}{30 \text{ feet}}$ $\newline$ Since there are $12$ inches in a foot, we need to convert $30$ feet into inches before we divide. $\newline$ $30$ feet $= 30 \times 12$ inches $\newline$ $30$ feet $= 360$ inches $\newline$ Scale factor $= \frac{10 \text{ inches}}{360 \text{ inches}}$
Calculate Scale Factor: Now, we calculate the scale factor. Scale factor = $\frac{10 \text{ inches}}{360 \text{ inches}}$ Scale factor = $\frac{1}{36}$
Find Width in Drawing: Next, we need to find the width of the floor in the scale drawing using the scale factor. Since the actual width of the floor is $24$ feet, we first convert that to inches. $\newline$ Actual width in inches = $24$ feet $\times 12$ inches/foot $\newline$ Actual width in inches = $288$ inches $\newline$ Now we apply the scale factor to find the width in the scale drawing. $\newline$ Width of scale drawing = Actual width in inches $\times$ Scale factor $\newline$ Width of scale drawing = $288$ inches $\times (1 / 36)$
Calculate Width: We calculate the width of the scale drawing. $\newline$ Width of scale drawing = $288$ inches $\times (1 / 36)$ $\newline$ Width of scale drawing = $8$ inches
Find Area in Drawing: Finally, we find the area of the floor in the scale drawing by multiplying the length and width of the scale drawing. $\newline$ Area of scale drawing = Length of scale drawing $\times$ Width of scale drawing $\newline$ Area of scale drawing = $10$ inches $\times$ $8$ inches
Calculate Area: We calculate the area of the scale drawing. $\newline$ Area of scale drawing = $10\,\text{inches} \times 8\,\text{inches}$ $\newline$ Area of scale drawing = $80\,\text{square inches}$