The problem is about calculating the error on the area of a rectangular field.
What is known is that the sides of the rectangle are 120 m and 180 m, and they have been measured with a 10 m measuring tape. The tape has a sensitivity of 2 cm.
Since the area is the product of the sides, one has to calculate its relative error to have its absolute error.
The absolute error is the product of the relative error times the area.
The relative error on the area is the sum of the relative errors on the sides.
The Attempt at a Solution
The whole point is what is the relative error on the rectangle sides. I'd say that this is the ratio of the sensitivity and the range of the measuring tape.
For instance, the first side has been measured by summing 12 measures, each of which has a sensitivity of 2 cm = 0.02 m. The absolute error is 12⋅0.02 m = 0.24 m, and the relative error is 12⋅0.02/120=0.02/10=0.002.
Likewise for the second side.
So the relative error on the area is 0.004 and the corresponding absolute error is 0.004⋅120⋅180=86.4 ≈ 90
I'm puzzled because the solution to the exercise says that the relative error is 0.002.
Maybe I'm not getting the part where one uses a short measuring instrument to measure a longer distance.
PS Actually the problem is about the price of the field, but this is obtained by multiplying the area by the price of a square meter. Since this is an exact number it won't affect the relative error, right?