The actual dimensions of a rectangle are 3cm by 8cm. Eric measures the sides to be 2.57cm by 8.02cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Calculate actual area: Calculate the actual area of the rectangle using the actual dimensions. Actual area = length * width = 3cm * 8cm = 24cm².Calculate measured area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = measured length * measured width = 2.57cm * 8.02cm = 20.594cm².Calculate absolute error: Calculate the absolute error in the area. Absolute error = |Actual area - Measured area| = |24cm² - 20.594cm²| = 3.406cm².Calculate relative error: Calculate the relative error by dividing the absolute error by the actual area and then converting it to a percentage. Relative error = (Absolute error / Actual area) * 100 = (3.406cm² / 24cm²) * 100.Perform calculation: Perform the calculation for the relative error. Relative error = (3.406 / 24) * 100 ≈ 14.1917%.Convert to decimal: Convert the relative error to a decimal to the nearest thousandth. Relative error (to the nearest thousandth) = 0.142 (rounded from 0.1417).

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The actual dimensions of a rectangle are
3cm by
8cm. Eric measures the sides to be
2.57cm by
8.02cm. In calculating the area, what is the relative error, to the nearest thousandth.
Answer:

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $8 \mathrm{~cm}$ . Eric measures the sides to be $2.57 \mathrm{~cm}$ by $8.02 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer:

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Algebra 2

Pythagorean Theorem and its converse

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Q. The actual dimensions of a rectangle are

3 \mathrm{~cm}

8 \mathrm{~cm}

. Eric measures the sides to be

2.57 \mathrm{~cm}

8.02 \mathrm{~cm}

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

\newline

Answer:

Calculate actual area: Calculate the actual area of the rectangle using the actual dimensions. $\newline$ Actual area = $\text{length} \times \text{width} = 3\,\text{cm} \times 8\,\text{cm} = 24\,\text{cm}^2$ .
Calculate measured area: Calculate the measured area of the rectangle using the measured dimensions. $\newline$ Measured area = measured length $\times$ measured width = $2.57\,\text{cm} \times 8.02\,\text{cm} = 20.594\,\text{cm}^2$ .
Calculate absolute error: Calculate the absolute error in the area. $\newline$ Absolute error = $|\text{Actual area} - \text{Measured area}| = |24\,\text{cm}^2 - 20.594\,\text{cm}^2| = 3.406\,\text{cm}^2$ .
Calculate relative error: Calculate the relative error by dividing the absolute error by the actual area and then converting it to a percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Actual area}) \times 100 = (3.406\,\text{cm}^2 / 24\,\text{cm}^2) \times 100$ .
Perform calculation: Perform the calculation for the relative error. $\newline$ Relative error = $(3.406 / 24) \times 100 \approx 14.1917\%$ .
Convert to decimal: Convert the relative error to a decimal to the nearest thousandth. $\newline$ Relative error (to the nearest thousandth) = $0.142$ (rounded from $0.1417$ ).