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Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the second map is 6 cm. 1 cm on the first map represents 2 km on the actual trail.


This problem has 4 parts. Please answer each part and show your work so I know how you got your answers. Thanks

AWhat is the scale factor from the map to the actual trail? (Please include work)
BWhat is the length of the actual trail? (Please include Work)

A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

CWhat is the scale factor from the first map to the second map? (Please include work)
DWhat are the side lengths of the landmark on the second map? (Please include work)

Anyone who gets these right will be marked the brainiest. Thanks everyone for your help.

Verified Answer :

Hagrid

Given: 

Two trail maps:

Trail on the first map = 8 cm
Trail on the second map = 6 cm

Scale on first map = 1 cm : 2 km

A) What is the scale factor from the map to the actual trail? 

For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km. 

The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm 

B) The length of the actual trail is 16 kilometers. 

Scale factor is the factor by which the original figure is smaller or larger.

  • A) The scale factor for the first is 1:200000.
  • B) The length of the actual trail is 16 kilometre.
  • C) Scale factor from the first map to the second map is 4:5.
  • D) The side lengths of the landmark on the second map are 2.4 mm, 3.2 mm, and 4 mm.

Given information

The length of the trail on the first map is 8 cm.

The length of the trail on the second map is 6 cm.

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

  • A)The scale factor from the map to the actual trail-

What is scale factor?

Scale factor is the factor by which the original figure is smaller or larger.

As for the first map, 1 cm represents the 2 kilometres.  There are 100000 cm in 1 kilometres. Thus the 2 kilometre has cm,

\(1=200000\)

Thus the scale factor for the first is 1:200000.

  • B) The length of the actual trail-

The length of the first trail is 8 cm.As there are 2 km on the actual trail for the 1 cm in first map. Thus the length of the actual trail is,

\(=8\times2\\=16\)

Hence the length of the actual trail is 16 kilometre.

  • C) The scale factor from the first map to the second map-

The second map has a represent the 16 kilometre actual trail in 6 cm on the map. Thus the scale factor of the second trail is,

\(6=16000000\\2=320000\)

The scale factor of the second trail is 2:320000.

The first trail and second trial both represents the same 16 kilometre actual trial on the map. Thus the scale factor from the first map to the second map is,

\(=\dfrac{\dfrac{1}{200000} }{\dfrac{2}{320000} } \\=\dfrac{4}{5}\)

Scale factor from the first map to the second map is 4:5.

  • D) The side lengths of the landmark on the second map-

A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

As, the scale factor from the first map to the second map is 4:5. Thus the length are multiplies by this ratio to get the side length of the landmark on second map.

\(=\dfrac{4}{5} \times3=2.4\\=\dfrac{4}{5} \times4=3.2\\ =\dfrac{4}{5} \times5=4\\\)

Hence the side lengths of the landmark on the second map are 2.4 mm, 3.2 mm, and 4 mm.

Hence,

  • A) The scale factor for the first is 1:200000.
  • B) The length of the actual trail is 16 kilometre.
  • C) Scale factor from the first map to the second map is 4:5.
  • D) The side lengths of the landmark on the second map are 2.4 mm, 3.2 mm, and 4 mm.

Learn more about the scale factor here;

https://brainly.com/question/8765466

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