Martha is having carpet installed in a rectangular room.She estimates the measurements of the room to be 13 ft by 19 ft. The actual measurements of the room are 12 ft by 18 ft. Which expression represents the relative error in the measurement of the area of the room
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To find the relative error in the measurement of the area of the room, you need to calculate the difference between the estimated area and the actual area, and then divide it by the actual area.
First, let's find the estimated area of the room using the estimated measurements:
Estimated Area = Length × Width
Estimated Area = 13 ft × 19 ft
Now, let's find the actual area of the room using the actual measurements:
Actual Area = Length × Width
Actual Area = 12 ft × 18 ft
To calculate the relative error, we need to find the difference between the estimated area and the actual area, and then divide it by the actual area:
Relative Error = (Estimated Area - Actual Area) / Actual Area
Substituting the values:
Relative Error = (13 ft × 19 ft - 12 ft × 18 ft) / (12 ft × 18 ft)
Simplifying the expression:
Relative Error = (247 ft² - 216 ft²) / (216 ft²)
Relative Error = 31 ft² / 216 ft²
Therefore, the expression that represents the relative error in the measurement of the area of the room is 31 ft² / 216 ft².