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Scale for 1.5 km road on map

Short answer

RF is 1/4000, so 1 cm equals 40 m. A diagonal scale 12.5 cm long reads 1 m up to 500 m; divide into five 100 m parts of 2.5 cm, subdivide left part into 10 m, and draw diagonals for 1 m steps.

A 1.5 km long road is indicated in a map by a length of 37.5 cm. Find the scale of the plot and indicate through a sketch how a suitable scale can be constructed to read upto 1 m in the map.

Scale (RF)

1.5 km =1500= 1500 m =1.5×105= 1.5 \times 10^{5} cm is shown by 37.5 cm.

RF=37.51.5×105=14000\text{RF} = \frac{37.5}{1.5 \times 10^{5}} = \frac{1}{4000}

so 1 cm on the map =40= 40 m on the ground.

Scale to read 1 m

A diagonal scale is suitable. Take a maximum reading of 500 m.

Length=500×1004000=12.5 cm\text{Length} = \frac{500 \times 100}{4000} = 12.5\ \text{cm}

100 m =2.5= 2.5 cm, 10 m =0.25= 0.25 cm, 1 m =0.025= 0.025 cm.

Sketch and construction

  1. Draw a line 12.5 cm long; divide it into 5 equal parts of 2.5 cm (100 m). Extend by one more division to the left of 0.
  2. Divide the left division into 10 equal parts (10 m each).
  3. Draw 10 horizontal lines through equal divisions of a vertical 2.5 cm high.
  4. Join the top of each sub-division with the next lower sub-division at the base (diagonals). Each horizontal line cuts a diagonal at 1 m steps.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+----+----+----+
   90..0  100  200  300  400  500 (m)

Example: 234 m is 200 m + 30 m + 4 m.

Answer: RF = 1/4000 (1 cm = 40 m); diagonal scale length 12.5 cm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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