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? Answer: in. ^(2)

Question

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? Answer: in.  ^(2)

Bytelearn · Accepted Answer

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. Scale factor = Length of scale drawing / Actual length of floor Scale factor = 10 inches / 30 feet Since there are 12 inches in a foot, we need to convert 30 feet into inches before we divide. 30 feet = 30 * 12 inches 30 feet = 360 inches Scale factor = 10 inches / 360 inchesCalculate Scale Factor: Now, we calculate the scale factor. Scale factor = 10 inches / 360 inches Scale factor = 1 / 36Find 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. Actual width in inches = 24 feet * 12 inches/foot Actual width in inches = 288 inches Now we apply the scale factor to find the width in the scale drawing. Width of scale drawing = Actual width in inches * Scale factor Width of scale drawing = 288 inches * (1 / 36)Calculate Width: We calculate the width of the scale drawing. Width of scale drawing = 288 inches * (1 / 36) Width of scale drawing = 8 inchesFind 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. Area of scale drawing = Length of scale drawing * Width of scale drawing Area of scale drawing = 10 inches * 8 inchesCalculate Area: We calculate the area of the scale drawing. Area of scale drawing = 10 inches * 8 inches Area of scale drawing = 80 square inches

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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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. $^{2}$