Question

An area of ground lying between a straight road and boundary has an actual area of 6250m². The area as measured on an old plan whose scale has been obliterated is 1000mm². What is the scale of the old plan?

a) 1:10
b) 1:25
c) 1:50
d) 1:100

Answer 1

The scale of the old plan is 1:25, which is found using the square root of the ratio of the area on the plan to the actual area, after converting to consistent units.

Step-by-step explanation:

The scale of an old plan can be found by comparing the actual area of a location with the area represented on the plan. The formula to calculate the scale factor of a map or plan is the square root of (area on plan/actual area). In this case, the actual area of the ground is 6250 m² and the plan shows it as 1000 mm².

First, we convert the actual area from square meters to square millimeters since the plan's area is in square millimeters:
6250 m² = 6250 × (1000 mm) × (1000 mm) = 6250 × 10¶ mm²

Now we can calculate the scale factor:
Scale factor = √(1000 mm² / 6250 × 10¶ mm²) = √(1/6250 × 10¶) = √(1/625) = 1/25
Hence, the scale of the old plan is 1:25.