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29 April, 23:28

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)

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  1. 29 April, 23:51
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    Step-by-step explanation:

    fractional uncertainty, to quantify the precision of a measurement for L and W is

    ΔL/L = 1/4 = 0.25 = 25%

    ΔW/W = 2/10 = 2/5 = 0.4 = 40%

    Now the area of triangle A = L*W = 4*10 = 40m^2

    The rules for propagation of error state that when two quantities are multiplied, their fractional uncertainties are added:

    So,

    ΔA/A = ΔL/L + ΔW/W = 0.25+0.4 = 0.65 = 65%

    Now we can compute uncertainty in the area, which is

    ΔA = A * (ΔA/A) = 40*0.65 = 26%

    Finally, we can write the area of the rectangle together with its uncertainty:

    A = 40m^2 ± 26%
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