The actual dimensions of a rectangle are 6 in by 4in. Carter measures the sides to be 5.75 in by 3.59in. In calculating the area, what is the relative error, to the nearest hundredth. Answer:

Calculate Actual Area: Calculate the actual area of the rectangle using the actual dimensions. The formula for the area of a rectangle is length × width. Actual area = 6 in × 4 in = 24 in².Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = 5.75 in × 3.59 in. Let's perform the multiplication to find the measured area. Measured area = 20.6425 in².Calculate Absolute Error: Calculate the absolute error by subtracting the measured area from the actual area. Absolute error = Actual area - Measured area. Absolute error = 24 in² - 20.6425 in². Absolute error = 3.3575 in².Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual area. Relative error = Absolute error / Actual area. Relative error = 3.3575 in² / 24 in². Let's perform the division to find the relative error. Relative error ≈ 0.1398958333.Convert to Percentage: Convert the relative error to a percentage and round to the nearest hundredth. Relative error (as a percentage) = Relative error × 100. Relative error (as a percentage) ≈ 0.1398958333 × 100. Relative error (as a percentage) ≈ 13.99%.

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The actual dimensions of a rectangle are 6 in by
4in. Carter measures the sides to be 5.75 in by
3.59in. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are $6$ in by $4 \mathrm{in}$ . Carter measures the sides to be $5$ . $75$ in by $3.59 \mathrm{in}$ . In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Full solution

Q. The actual dimensions of a rectangle are

6

in by

4 \mathrm{in}

. Carter measures the sides to be

5

75

in by

3.59 \mathrm{in}

. In calculating the area, what is the relative error, to the nearest hundredth.

\newline

Answer:

Calculate Actual Area: Calculate the actual area of the rectangle using the actual dimensions. $\newline$ The formula for the area of a rectangle is $\text{length} \times \text{width}$ . $\newline$ Actual area = $6 \, \text{in} \times 4 \, \text{in} = 24 \, \text{in}^2$ .
Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. $\newline$ Measured area = $5.75 \, \text{in} \times 3.59 \, \text{in}$ . $\newline$ Let's perform the multiplication to find the measured area. $\newline$ Measured area = $20.6425 \, \text{in}^2$ .
Calculate Absolute Error: Calculate the absolute error by subtracting the measured area from the actual area. $\newline$ Absolute error = Actual area - Measured area. $\newline$ Absolute error = $24 \, \text{in}^2 - 20.6425 \, \text{in}^2$ . $\newline$ Absolute error = $3.3575 \, \text{in}^2$ .
Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual area. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual area}}$ . $\newline$ Relative error = $\frac{3.3575 \, \text{in}^2}{24 \, \text{in}^2}$ . $\newline$ Let's perform the division to find the relative error. $\newline$ Relative error $\approx 0.1398958333$ .
Convert to Percentage: Convert the relative error to a percentage and round to the nearest hundredth. $\newline$ Relative error (as a percentage) = Relative error $\times 100$ . $\newline$ Relative error (as a percentage) $\approx 0.1398958333 \times 100$ . $\newline$ Relative error (as a percentage) $\approx 13.99\%$ .