The rectangular floor of a classroom is 20 feet in length and 32 feet in width. A scale drawing of the floor has a length of 5 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 20 feet in length and 32 feet in width. A scale drawing of the floor has a length of 5 inches. What is the area, in square inches, of the floor in the scale drawing? Answer: in.  ^(2)

Bytelearn · Accepted Answer

Find Scale Factor: First, we need to find the scale factor that relates the actual size of the classroom to the size of the scale drawing. We can do this by dividing the length of the classroom in the scale drawing by the actual length of the classroom. Scale factor = Length of the classroom in the scale drawing / Actual length of the classroom Scale factor = 5 inches / 20 feetConvert Actual Length: Since we need to have the same units to divide, we should convert the actual length of the classroom from feet to inches. There are 12 inches in a foot. Actual length of the classroom in inches = 20 feet * 12 inches/foot Actual length of the classroom in inches = 240 inchesCalculate Scale Factor: Now we can calculate the scale factor. Scale factor = 5 inches / 240 inches Scale factor = 1/48Find Width in Drawing: Next, we need to find the width of the classroom in the scale drawing using the scale factor. Since we know the actual width of the classroom is 32 feet, we first convert that to inches. Actual width of the classroom in inches = 32 feet * 12 inches/foot Actual width of the classroom in inches = 384 inchesCalculate Area: Now we can find the width of the classroom in the scale drawing. Width of the classroom in the scale drawing = Actual width of the classroom in inches * Scale factor Width of the classroom in the scale drawing = 384 inches * 1/48 Width of the classroom in the scale drawing = 8 inchesFinally, we can calculate the area of the classroom in the scale drawing by multiplying the length and width in the scale drawing. Area of the scale drawing = Length of the scale drawing * Width of the scale drawing Area of the scale drawing = 5 inches * 8 inches Area of the scale drawing = 40 square inches

The rectangular floor of a classroom is $20$ feet in length and $32$ feet in width. A scale drawing of the floor has a length of $5$ 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 $20$ feet in length and $32$ feet in width. A scale drawing of the floor has a length of $5$ inches. What is the area, in square inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in. $^{2}$