The scale of a map is 1 cm represents 25 m - OCR - GCSE Maths - Question 2 - 2017 - Paper 1
Question 2
The scale of a map is 1 cm represents 25 m.
(i) The length of a path is 240 m.
Work out the length, in centimetres, of the path on the map.
(ii) The scale 1 cm re... show full transcript
Worked Solution & Example Answer:The scale of a map is 1 cm represents 25 m - OCR - GCSE Maths - Question 2 - 2017 - Paper 1
Step 1
The length of a path is 240 m.
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Answer
To calculate the length on the map, we use the scale given: 1 cm represents 25 m.
First, we need to convert 240 m into cm for the map.
Using the conversion:
extLengthonmap(cm)=Scale (meters per cm)Length in meters
Thus,
Length on map (cm)=25240=9.6 cm
Therefore, the length of the path on the map is 9.6 cm.
Step 2
The scale 1 cm represents 25 m can be written in the form 1:k.
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Answer
To express the scale in the form 1:k, we set up a proportion. Since 1 cm represents 25 m, we can find k by stating:
1:k=1:25
This implies that:
k=25
Thus, the value of k is 25.
Step 3
A new play area must be no more than 150 m from B, closer to AD than to CD.
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Answer
To locate the new play area, we need to follow these instructions:
Draw a circle with a radius of 150 m around Point B. This represents the maximum distance from B to the new play area.
Next, bisect the segment AD and the segment CD. This will help determine the area closer to AD.
Shade the region that falls within the circle and also closer to line AD than line CD.
All construction lines must be clearly marked to indicate the boundaries defined by these criteria.
