Question

The lengths of the rectangle have been measured to the nearest tenth of a centimetre. Work out the following, writing down all the figures on your calculator display: a) The upper bound for the area of the rectangle. b) The lower bound for the perimeter of the rectangle.

length of rectangle 9.8
with of rectangle 4.3​

Answer 1

• area < 42.8475 cm²
• perimeter ≥ 28.00 cm

Explanation:

You want the maximum area and the minimum perimeter that could apply to a rectangle measured as 9.8 cm long by 4.3 cm wide.

Error

The possible error in a measurement is presumed to be half of the place value of the least-significant digit. For a measurement given to the nearest tenth centimeter, the possible error is 5 hundredths of a centimeter.

Maximum area

The area will be a maximum if both dimensions are at their maximum:

A = LW

A = (9.8 +.05)(4.3 +.05) cm² = 42.8475 cm² . . . . maximum

Minimum perimeter

The perimeter will be a minimum if both of the dimensions are at their minimum:

P = 2(L +W)

P = 2((9.8 -0.05) +(4.3 -0.05)) cm = 28.00 cm . . . . minimum

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Additional comment

The attached calculator display does not show trailing zeros. The sum of numbers expressed to a precision of hundredths of a centimeter will have a precision of hundredths of a cm. Two digits after the decimal point will be significant for the perimeter. (The maximum and minimum measurement values are treated as exact.)