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Alecsey [184]
3 years ago
5

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.
Mathematics
1 answer:
Tomtit [17]3 years ago
7 0

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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