Question

a rectangle has measured dimensions of 2.76 miles and 4.37 miles. taking measurement error into account, what are the minimum and maximum possible areas? minimum possible area = mi² maximum possible area = mi²

Explanation:

Step1: Determine the measurement error

The measurement error for a measurement \(x\) is \(\pm0.005\) (since when measuring to the nearest \(0.01\), the error is half of \(0.01\)).
For length \(l = 2.76\) miles, the maximum length \(l_{max}=2.76 + 0.005=2.765\) miles and the minimum length \(l_{min}=2.76- 0.005 = 2.755\) miles.
For width \(w = 4.37\) miles, the maximum width \(w_{max}=4.37+0.005 = 4.375\) miles and the minimum width \(w_{min}=4.37 - 0.005=4.365\) miles.

Step2: Calculate the maximum - area

The area of a rectangle is \(A=l\times w\).
The maximum area \(A_{max}=l_{max}\times w_{max}\)
\(A_{max}=2.765\times4.375\)

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Step3: Calculate the minimum - area

The minimum area \(A_{min}=l_{min}\times w_{min}\)
\(A_{min}=2.755\times4.365\)

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Answer:

Maximum possible area \(=12.096875\) \(mi^{2}\), Minimum possible area \(=12.025575\) \(mi^{2}\)