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The actual dimensions of a rectangle are 
9ft by 
6ft. Eric measures the sides to be 
8.91ft by 
6.22ft. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are 9ft 9 \mathrm{ft} by 6ft 6 \mathrm{ft} . Eric measures the sides to be 8.91ft 8.91 \mathrm{ft} by 6.22ft 6.22 \mathrm{ft} . In calculating the area, what is the relative error, to the nearest hundredth.\newlineAnswer:

Full solution

Q. The actual dimensions of a rectangle are 9ft 9 \mathrm{ft} by 6ft 6 \mathrm{ft} . Eric measures the sides to be 8.91ft 8.91 \mathrm{ft} by 6.22ft 6.22 \mathrm{ft} . In calculating the area, what is the relative error, to the nearest hundredth.\newlineAnswer:
  1. Calculate actual area: Calculate the actual area of the rectangle using the actual dimensions.\newlineThe formula for the area of a rectangle is length×width\text{length} \times \text{width}.\newlineActual area = 9ft×6ft9\,\text{ft} \times 6\,\text{ft}.
  2. Calculate actual area: Perform the calculation for the actual area. Actual area = 9ft×6ft=54ft29\,\text{ft} \times 6\,\text{ft} = 54\,\text{ft}^2.
  3. Calculate measured area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = 8.91ft×6.22ft.8.91\,\text{ft} \times 6.22\,\text{ft}.
  4. Calculate measured area: Perform the calculation for the measured area. Measured area = 8.91ft×6.22ft55.43ft28.91\,\text{ft} \times 6.22\,\text{ft} \approx 55.43\,\text{ft}^2.
  5. Calculate absolute error: Calculate the absolute error by subtracting the actual area from the measured area. Absolute error = Measured areaActual area|\text{Measured area} - \text{Actual area}|.
  6. Calculate absolute error: Perform the calculation for the absolute error. Absolute error = 55.43ft254ft21.43ft2|55.43\text{ft}^2 - 54\text{ft}^2| \approx 1.43\text{ft}^2.
  7. Calculate relative error: Calculate the relative error by dividing the absolute error by the actual area.\newlineRelative error = Absolute errorActual area\frac{\text{Absolute error}}{\text{Actual area}}.
  8. Calculate relative error: Perform the calculation for the relative error. Relative error = 1.43ft254ft20.02648\frac{1.43\,\text{ft}^2}{54\,\text{ft}^2} \approx 0.02648.
  9. Convert relative error: Convert the relative error to a percentage and round to the nearest hundredth.\newlineRelative error (percentage) = 0.02648×1002.65%0.02648 \times 100 \approx 2.65\%.

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