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The length and width of a rectangle are measured to be 8 cm and 5 cm respectively, to the nearest centimetre - HSC - SSCE Mathematics Standard - Question 12 - 2023 - Paper 1

Question 12

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The length and width of a rectangle are measured to be 8 cm and 5 cm respectively, to the nearest centimetre. What are the lower and upper bounds for the area of th... show full transcript

Worked Solution & Example Answer:The length and width of a rectangle are measured to be 8 cm and 5 cm respectively, to the nearest centimetre - HSC - SSCE Mathematics Standard - Question 12 - 2023 - Paper 1

Step 1

Calculate the Lower Bound Area

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Answer

The lower bound for the length and width is:

Length = 8 cm - 0.5 cm = 7.5 cm
Width = 5 cm - 0.5 cm = 4.5 cm

The lower bound area is calculated as:

$ext{Area}_{ ext{lower}} = ext{Length}_{ ext{lower}} imes ext{Width}_{ ext{lower}} = 7.5 imes 4.5 = 33.75 ext{ cm}²$

Step 2

Calculate the Upper Bound Area

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Answer

The upper bound for the length and width is:

Length = 8 cm + 0.5 cm = 8.5 cm
Width = 5 cm + 0.5 cm = 5.5 cm

The upper bound area is calculated as:

$ext{Area}_{ ext{upper}} = ext{Length}_{ ext{upper}} imes ext{Width}_{ ext{upper}} = 8.5 imes 5.5 = 46.75 ext{ cm}²$

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