The actual dimensions of a rectangle are 6ft by 2ft. Alex measures the sides to be 6.22ft by 1.68ft. In calculating the area, what is the relative error, to the nearest hundredth. Answer:

Question

The actual dimensions of a rectangle are  6ft by  2ft. Alex measures the sides to be  6.22ft by  1.68ft. In calculating the area, what is the relative error, to the nearest hundredth. Answer:

Bytelearn · Accepted 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 = 6ft × 2ft = 12ft².Calculate Measured Area: Calculate the measured area of the rectangle using the measured dimensions. Measured area = 6.22ft × 1.68ft. Let's perform the multiplication to find the measured area. Measured area = 10.4496ft².Calculate Absolute Error: Calculate the absolute error by subtracting the actual area from the measured area. Absolute error = |Measured area - Actual area|. Absolute error = |10.4496ft² - 12ft²|. Absolute error = |-1.5504ft²|. Since we are looking for the absolute value, we take the positive value of the result. Absolute error = 1.5504ft².Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual area. Relative error = Absolute error / Actual area. Relative error = 1.5504ft² / 12ft². Let's perform the division to find the relative error. Relative error ≈ 0.1292.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) ≈ 0.1292 × 100. Relative error (as a percentage) ≈ 12.92%. When rounded to the nearest hundredth, the relative error is 12.92%.

The actual dimensions of a rectangle are $6 \mathrm{ft}$ by $2 \mathrm{ft}$ . Alex measures the sides to be $6.22 \mathrm{ft}$ by $1.68 \mathrm{ft}$ . In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ 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 2ft 2 \mathrm{ft} 2ft. Alex measures the sides to be 6.22ft 6.22 \mathrm{ft} 6.22ft by 1.68ft 1.68 \mathrm{ft} 1.68ft. In calculating the area, what is the relative error, to the nearest hundredth.\newlineAnswer:

The actual dimensions of a rectangle are $6 \mathrm{ft}$ by $2 \mathrm{ft}$ . Alex measures the sides to be $6.22 \mathrm{ft}$ by $1.68 \mathrm{ft}$ . In calculating the area, what is the relative error, to the nearest hundredth. $\newline$ Answer: