Question

ok, 1cm =2km in actual length, 8cm length I'm first map, 6 cm length in 2 map, how do I figure out the actual length?

Answer 1

Answer:

• (a)(i)1:200,000 (ii)16km

,

• (b)i)4:3 (ii)2.25mm, 3mm and 3.75mm.

Explanation:

Part A

First, we determine the scale factor from the map to the actual trail.

$\text{Map:Actual Trail=1cm:2km}$

Next, we convert to same units:

$\begin{gathered} 1\operatorname{cm}\colon2\operatorname{km}=1\operatorname{cm}\colon2000m \\ =1\operatorname{cm}\colon200,000\operatorname{cm} \\ =1\colon200,000 \end{gathered}$

The scale factor from the map to the actual trail is 1:200,000.

1 cm on the first map represents 2km on the actual trail.

The length of the trail on the first map = 8cm

Let the length of the actual trail = x

$\begin{gathered} \frac{1\operatorname{cm}}{2\operatorname{km}}=\frac{8\operatorname{cm}}{\text{x km}} \\ x=2\times8=16\operatorname{km} \end{gathered}$

The length of the actual trail is 16km.

Part B

The length of the trail on the first map = 8cm

The length of the trail on the second map = 6cm

The scale factor from the first map to the second map = 8:6 = 4:3

The dimensions of the triangle on the first map are 3mm, 4mm, and 5mm.

$\begin{gathered} \frac{4}{3}=\frac{3}{x} \\ 4x=9 \\ x=2.25\operatorname{mm} \end{gathered}$

Similarly:

$\begin{gathered} \frac{4}{3}=\frac{4}{y} \\ 4y=12 \\ y=3\operatorname{mm} \end{gathered}$

Finally:

$\begin{gathered} \frac{4}{3}=\frac{5}{z} \\ 4z=15 \\ z=3.75\operatorname{mm} \end{gathered}$

The side lengths of the landmarks on the second map are 2.25mm, 3mm, and 3.75mm.