The length and width of a rectangle are measured as 27 cm and 50 cm, respectively, with an error in measurement of at most 0.1 c
m in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
1 answer:
Answer:
7.7cm
Step-by-step explanation:
Area of a rectangle is expressed as
A = Length × Width
A = LW
Let dL and dW be the errors in the measurements.
If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.
The area of the rectangle with error will be expressed as A = LdW + WdL
Given L = 27cm and W = 50cm
A = 27(0.1)+50(0.1)
A = 2.7+5.0
A = 7.7cm
Hence, the maximum error in the calculated area of the rectangle is 7.7cm
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