If a line of length 5cm represents 40km, then we can find the scale factor by dividing the length of the line on the map by the actual distance it represents:
Scale factor = 5cm / 40km = 1cm / 8km
To find out how many kilometers a line of length 7 1/2 cm represents, we can multiply the length of the line by the scale factor:
7 1/2 cm x 1cm / 8km = (15/2)cm x 1cm / 8km = 15/16 km
Therefore, a line of length 7 1/2 cm represents 15/16 km or approximately 0.938 km.