Question

Two points are separated on the ground by a distance of 43 km. Can they be placed on a 1 / 25000th map with dimensions 1.32 m on0.85 m?

Answer 1

No

Explanation:

The distance between the two points on the ground = 43km

`\text{Scale}=(1)/(25000)`

First, we calculate the distance between the two points in meters.

• 43km = 43,000 m.

Next, determine the distance it will take using the scale.

`\begin{gathered} (1)/(25000)=(x)/(43000) \\ 25000x=43000 \\ x=(43000)/(25000) \\ x=1.72m \end{gathered}`

The distance between the points using the scale is 1.72m.

Next, we see that the dimensions (1.32 m by 0.85 m) are smaller than the length.

As a final check, calculate the length of the diagonal of the map. The diagonal is usually the longest part.

`\text{Diagonal}=\sqrt[]{1.32^2+0.85^2}=1.57m`

Since 1.57m is still less than 1.72m, the two points cannot be placed on the map.