The actual dimensions of a rectangle are 3cm by 2cm. Eric measures the sides to be 3.49cm by 2.13cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Question

The actual dimensions of a rectangle are  3cm by  2cm. Eric measures the sides to be  3.49cm by  2.13cm. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Bytelearn · Accepted Answer

Calculate Actual Area: To find the relative error, we first need to calculate the actual area and the measured area of the rectangle. The actual area (A_actual) is the product of the actual length and width. A_actual = 3cm * 2cmCalculate Measured Area: Now we calculate the measured area (A_measured) using the measured dimensions. A_measured = 3.49cm * 2.13cmFind Absolute Error: Perform the calculations for both actual and measured areas. A_actual = 3cm * 2cm = 6cm² A_measured = 3.49cm * 2.13cm = 7.4327cm²Calculate Absolute Error: The absolute error is the difference between the measured area and the actual area. Absolute error = |A_measured - A_actual|Find Relative Error: Calculate the absolute error using the values obtained. Absolute error = |7.4327cm² - 6cm²| = |1.4327cm²| = 1.4327cm²Calculate Relative Error: The relative error is the absolute error divided by the actual area. Relative error = Absolute error / A_actualPerform Division: Now we calculate the relative error with the values we have. Relative error = 1.4327cm² / 6cm²Round to Nearest Thousandth: Perform the division to find the relative error. Relative error = 1.4327cm² / 6cm² ≈ 0.2387833333To express the relative error to the nearest thousandth, we round the result to three decimal places. Relative error ≈ 0.239

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $2 \mathrm{~cm}$ . Eric measures the sides to be $3.49 \mathrm{~cm}$ by $2.13 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer:

Full solution

More problems from Percent error: word problems

Related topics

The actual dimensions of a rectangle are 3 cm 3 \mathrm{~cm} 3 cm by 2 cm 2 \mathrm{~cm} 2 cm. Eric measures the sides to be 3.49 cm 3.49 \mathrm{~cm} 3.49 cm by 2.13 cm 2.13 \mathrm{~cm} 2.13 cm. In calculating the area, what is the relative error, to the nearest thousandth.\newlineAnswer:

The actual dimensions of a rectangle are $3 \mathrm{~cm}$ by $2 \mathrm{~cm}$ . Eric measures the sides to be $3.49 \mathrm{~cm}$ by $2.13 \mathrm{~cm}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer: