The actual dimensions of a rectangle are 6ft by 10ft. David measures the sides to be 6.23ft by 9.78ft. In calculating the area, what is the relative error, to the nearest thousandth. Answer:

Question

The actual dimensions of a rectangle are  6ft by  10ft. David measures the sides to be  6.23ft by  9.78ft. 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 = 6ft * 10ftCalculate Measured Area: Now, let's calculate the measured area (A_measured) using David's measurements. A_measured = 6.23ft * 9.78ftFind Absolute Error: Perform the calculations for both the actual area and the measured area. A_actual = 6ft * 10ft = 60ft² A_measured = 6.23ft * 9.78ft ≈ 60.944ft²Calculate Absolute Error: Next, we need to find the absolute error, which 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 we have. Absolute error = |60.944ft² - 60ft²| ≈ 0.944ft²Calculate Relative Error: To find the relative error, we divide the absolute error by the actual area and then multiply by 100 to get a percentage. Relative error = (Absolute error / A_actual) * 100Now, let's perform the calculation for the relative error. Relative error ≈ (0.944ft² / 60ft²) * 100 ≈ 1.573% (rounded to the nearest thousandth)

The actual dimensions of a rectangle are $6 \mathrm{ft}$ by $10 \mathrm{ft}$ . David measures the sides to be $6.23 \mathrm{ft}$ by $9.78 \mathrm{ft}$ . 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 6ft 6 \mathrm{ft} 6ft by 10ft 10 \mathrm{ft} 10ft. David measures the sides to be 6.23ft 6.23 \mathrm{ft} 6.23ft by 9.78ft 9.78 \mathrm{ft} 9.78ft. In calculating the area, what is the relative error, to the nearest thousandth.\newlineAnswer:

The actual dimensions of a rectangle are $6 \mathrm{ft}$ by $10 \mathrm{ft}$ . David measures the sides to be $6.23 \mathrm{ft}$ by $9.78 \mathrm{ft}$ . In calculating the area, what is the relative error, to the nearest thousandth. $\newline$ Answer: