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The actual dimensions of a rectangle are 6 in by 9 in. Eric measures the sides to be 5.96 in by 8.75 in. In calculating the area, what is the relative error, to the nearest hundredth.
Answer:

The actual dimensions of a rectangle are $6$ in by $9$ in. Eric measures the sides to be $5$ . $96$ in by $8$ . $75$ in. In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Circles: word problems

Full solution

Q. The actual dimensions of a rectangle are

6

in by

9

in. Eric measures the sides to be

5

.

96

in by

8

.

75

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

\newline

Answer:

Calculate Actual Area: First, we need to calculate the actual area of the rectangle using the actual dimensions. $\newline$ Actual area = $\text{length} \times \text{width}$ $\newline$ Actual area = $6 \, \text{in} \times 9 \, \text{in}$ $\newline$ Actual area = $54 \, \text{in}^2$
Calculate Measured Area: Next, we calculate the measured area of the rectangle using the measured dimensions. $\newline$ Measured area $= \text{measured length} \times \text{measured width}$ $\newline$ Measured area $= 5.96 \, \text{in} \times 8.75 \, \text{in}$ $\newline$ Measured area $= 52.15 \, \text{in}^2$
Find Absolute Error: Now, we find the absolute error in the area by subtracting the measured area from the actual area. $\newline$ Absolute error $= \text{Actual area} - \text{Measured area}$ $\newline$ Absolute error $= 54 \text{ in}^2 - 52.15 \text{ in}^2$ $\newline$ Absolute error $= 1.85 \text{ in}^2$
Find Relative Error: To find the relative error, we divide the absolute error by the actual area and then multiply by $100$ to get the percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Actual area}) \times 100$ $\newline$ Relative error = $(1.85 \, \text{in}^2 / 54 \, \text{in}^2) \times 100$ $\newline$ Relative error = $0.034259259 \times 100$ $\newline$ Relative error = $3.4259259\%$
Round Relative Error: Finally, we round the relative error to the nearest hundredth. $\newline$ Relative error $\approx 3.43\%$

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