This rectangle represents a tabletop. Its measured length is 48.5 ft, and its measured width is 36.5 ft.The relative error of these measured dimensions is 0.04. What is the relative error when computing the area of the tabletop?
a. 0.0082
b. 0.082
c. 0.82
d. 8.2
I think the answer's supposed to be b., but how do you get it?
(1.04)^2 -1 = 1.082 -1 = 0.082
To find the relative error when computing the area of the tabletop, we first need to calculate the relative error of each dimension, and then use those relative errors to calculate the relative error of the area.
1. Relative error of the length:
Relative error is calculated by dividing the absolute error by the measured value.
Absolute error = Relative error * measured value
Absolute error of the length = 0.04 * 48.5 = 1.94 ft
Relative error of the length = Absolute error of the length / measured length = 1.94 / 48.5 = 0.04
2. Relative error of the width:
Absolute error of the width = 0.04 * 36.5 = 1.46 ft
Relative error of the width = Absolute error of the width / measured width = 1.46 / 36.5 = 0.04
3. Calculate the area of the tabletop:
Area = length * width = 48.5 ft * 36.5 ft = 1770.25 ft²
4. Relative error of the area:
Absolute error of the area = Absolute error of the length + Absolute error of the width
Absolute error of the area = 1.94 ft + 1.46 ft = 3.40 ft²
Relative error of the area = Absolute error of the area / area = 3.40 / 1770.25 ≈ 0.0019
Based on the calculations, the relative error when computing the area of the tabletop is approximately 0.0019. Therefore, the correct answer is not b. 0.082, but rather there seems to be a discrepancy in the provided options.