Question

Suppose I measure the length and width of a rectangle, and get L = 4 +/- 1 m and W = 10 +/- 2m. What is the uncertainty (not fractional uncertainty!) in the area of the rectangle? (recall A = LW)

Answer 1

To calculate the uncertainty in the area of a rectangle, determine the maximum and minimum possible values for the area by using the upper and lower bounds of the length and width. The uncertainty in the area is the difference between the maximum and minimum area.

Step-by-step explanation:

To calculate the uncertainty in the area of a rectangle, we need to determine the maximum and minimum possible values for the area. The maximum area occurs when the length and width are both at their upper bounds, and the minimum area occurs when they are both at their lower bounds.

Maximum area: (L + ΔL) × (W + ΔW) = (4 + 1) × (10 + 2) = 5 × 12 = 60 m²

Minimum area: (L - ΔL) × (W - ΔW) = (4 - 1) × (10 - 2) = 3 × 8 = 24 m²

The uncertainty in the area is the difference between the maximum and minimum area: 60 m² - 24 m² = 36 m². Therefore, the uncertainty in the area of the rectangle is 36 square meters.