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 find the length on the map, we use the given scale of 1 cm representing 25 m. We can set up the following proportion:
extLengthonmap(cm)=Scale (m/cm)Length of path (m)
Substituting the values, we get:
Length on map (cm)=25 m/cm240 m=9.6 cm
Thus, 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 find the value of k, we can set up the relationship:
1 cm:25 m=1:k
From this, we can see that:
k=25
Therefore, 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 construct the shaded region for the new play area:
Draw an arc with a radius of 6 cm from point B (since 150 m corresponds to 6 cm) meeting lines AB and BC.
From points A, D, and C, draw the perpendicular bisector of line segment AD.
Next, draw the perpendicular bisector of line segment CD.
The shaded region will be the overlapping area where these conditions are satisfied and will encompass the area closer to AD than to CD, ensuring that it is no more than 150 m from point B.
