Exercise 1 solution

Ground distance (m) = centimetres on the map x scale / 100.

(a) 4.8 x 25,000 / 100 = 1,200 m (1.2 km). Check: 1 cm = 250 m, so 4.8 x 250 = 1,200.
(b) 6.4 x 50,000 / 100 = 3,200 m (3.2 km). Check: 1 cm = 500 m, so 6.4 x 500 = 3,200.
(c) 3.2 x 25,000 / 100 = 800 m.
(d) 22 x 25,000 / 100 = 5,500 m (5.5 km), the length of the winding path.

A ruler underestimates (d): a straight line between the ends of a winding path is shorter than the path itself. A ruler is fine for (a) to (c) if those are straight-line measurements.

Python check:

def map_to_ground(cm, scale):
    return cm * scale / 100

for cm, scale in [(4.8, 25000), (6.4, 50000), (3.2, 25000), (22, 25000)]:
    print(map_to_ground(cm, scale))

Output:
1200.0
3200.0
800.0
5500.0