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A rectangular sportsground has been drawn to scale on a 1-cm grid as shown - HSC - SSCE Mathematics Standard - Question 25 - 2021 - Paper 1

Question 25

A rectangular sportsground has been drawn to scale on a 1-cm grid as shown. The scale used is 1:3000. Kerry took 12 minutes to walk around the perimeter of this spo... show full transcript

Worked Solution & Example Answer:A rectangular sportsground has been drawn to scale on a 1-cm grid as shown - HSC - SSCE Mathematics Standard - Question 25 - 2021 - Paper 1

Step 1

Calculate the perimeter of the diagram

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Answer

The perimeter can be calculated using the formula for the perimeter of a rectangle:

$P = 2 imes (length + width)$

From the diagram, the length is 8 cm and the width is 5 cm. Thus,

$P = 2 imes (8 + 5) = 2 imes 13 = 26 ext{ cm}$

Step 2

Convert the perimeter to actual distance

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Using the scale of 1 cm = 3000 cm (or 30 m), the actual perimeter in metres is:

$ext{Actual perimeter} = 26 ext{ cm} imes 3000 = 78000 ext{ cm} = 780 ext{ m}$

Step 3

Calculate Kerry's speed

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Answer

Kerry took 12 minutes to walk around the perimeter. To find the speed in km/h, first convert the distance to km:

$780 ext{ m} = 0.78 ext{ km}$

Now, speed is calculated as:

$ext{Speed} = \frac{Distance}{Time} = \frac{0.78 ext{ km}}{\frac{12}{60} ext{ hours}} = \frac{0.78 ext{ km}}{0.2 ext{ hours}} = 3.9 ext{ km/h}$

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