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Diagonal scale: Kathmandu-Pokhara highway map

Short answer

RF is 1/4,000,000 and scale length is 15 cm. Use six 100 km divisions of 2.5 cm, subdivide left part into 10 km, and add diagonals for 1 km. Mark 224 as 200+20+4, 338 as 300+30+8, 459 as 400+50+9, and 579 as 500+70+9.

The distance between Kathmandu and Pokhara is 200 km. In a highway map it is represented by a line 5 cm long. Find its R.F. Draw a diagonal scale to show single km and maximum 600 km. Indicate the following distances: a) 224 km b) 338 km c) 459 km d) 579 km.

RF

200 km =2×107= 2 \times 10^7 cm is shown by 5 cm.

RF=52×107=14,000,000\text{RF} = \frac{5}{2 \times 10^{7}} = \frac{1}{4{,}000{,}000}

Scale length

600×1054×106=15 cm\frac{600 \times 10^{5}}{4 \times 10^{6}} = 15\ \text{cm}

So 100 km =2.5= 2.5 cm, 10 km =0.25= 0.25 cm and 1 km =0.025= 0.025 cm.

Construction

  1. Draw a 15 cm line and divide it into 6 main divisions of 2.5 cm (100 km). Mark 0 at the end of the first division and 100, 200 ... 500 for the others.
  2. Divide the first main division into 10 parts of 0.25 cm (10 km each).
  3. On the end verticals mark 10 equal divisions (height 2.5 cm) and draw 10 horizontal lines.
  4. Draw the diagonals from the top of each sub-division to the next lower sub-division on the base line. A step on the diagonal between two horizontal lines is 1 km.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+---+---+---+---+---+---+---+-+
   90..0   100  200  300  400  500 (km)

Distances

DistanceSplitVerticalDiagonal fromHorizontal line
(a) 224 km200 + 20 + 4200204th
(b) 338 km300 + 30 + 8300308th
(c) 459 km400 + 50 + 9400509th
(d) 579 km500 + 70 + 9500709th

The required length is measured between the vertical line and the point where the diagonal meets the horizontal line.

Answer: RF = 1/4,000,000; scale length = 15 cm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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