If the area of a rectangle is calculated as 50 m² with a length of 10 m and an u

If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?

If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?

Step 1: Identify the formula for the area of a rectangle, which is Area = Length × Width.
Step 2: In this case, we know the area is 50 m² and the length is 10 m.
Step 3: Since the width is not given, we can find it using the area formula: Width = Area / Length = 50 m² / 10 m = 5 m.
Step 4: Understand that the uncertainty in the area can be calculated using the formula: Uncertainty in Area = 2 × Length × Uncertainty in Length.
Step 5: Substitute the values into the formula: Uncertainty in Area = 2 × 10 m × 0.1 m = 2 m².
Step 6: Conclude that the uncertainty in the area is 2 m².

Area Calculation – Understanding how to calculate the area of a rectangle using the formula Area = Length × Width.
Propagation of Uncertainty – Applying the rules of uncertainty propagation to determine how uncertainties in measurements affect calculated results.