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Answer :
Final answer:
The actual dimensions of a room from a drawing with a 68 inches: 1 inch scale, measuring 3 7/8 inches by 2 5/8 inches, are approximately 21.96 feet by 14.88 feet. The area of the room is about 326.92 square feet.
Explanation:
To find the actual dimensions of the room using a scale factor, we first need to use the given scale of 68 inches corresponds to 1 inch on the drawing. The room measures 3 7/8 inches by 2 5/8 inches on the drawing.
First, we convert 3 7/8 inches to a decimal: 3 + 7/8 = 3 + 0.875
= 3.875 inches.
Then, we convert 2 5/8 inches to a decimal: 2 + 5/8 = 2 + 0.625
= 2.625 inches.
Now, we use the scale factor to find the actual dimensions. The scale ratio is 68:1, which means every 1 inch on the drawing represents 68 inches of actual length. Therefore, we multiply 3.875 inches and 2.625 inches each by 68.
Actual length = 3.875 x 68
= 263.5 inches
Actual width = 2.625 x 68
= 178.5 inches
To convert inches to feet (since there are 12 inches in a foot), we divide by 12:
Actual length in feet = 263.5 / 12
≈ 21.96 feet
Actual width in feet = 178.5 / 12
≈ 14.88 feet
Next, to find the area of the room in square feet, we multiply the actual length by the actual width:
Area = 21.96 feet x 14.88 feet
≈ 326.92 square feet
Therefore, the actual dimensions are approximately 21.96 feet by 14.88 feet and the area is about 326.92 square feet.
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