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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.

(a) A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm. What is the scale factor from the first map to the second map? Show your work. It may help you to “draw” out the two maps and label the trails.

(b) What are the side lengths of the landmark on the second map? Show your work. It may help you to “draw” out the two maps and label the trails.

Answer :

Edufirst

Answer:

  • (a) 3cm : 4 cm

  • (b) 2.25mm

              3mm

              3.75mm

Explanation:

(a) What is the scale factor from the first map to the second map?

You might “draw” out the two maps and label the trails as suggested but it is not necessary.

The scale factor is determined by the lengths of the trails on the first map and the second maps.

The scale factor from the first map to the second map is the ratio of a lenght in the second map to the corresponding legth on the first map.

  • scale factor = length on the second map / length on the first map
  • scale factor = 6cm / 8 cm = 3cm/4cm, or 3cm : 4cm.

Note that means the if you have a length on the first map you can find the corresponding length on the second by multiplyin the former by 3/4.

(b) What are the side lengths of the landmark on the second map?

Now you must use the scale factor 3cm/4cm. Multiply each length on the first map by 3cm/4cm to find the legth on the second map.

Length on the first map        Length on the second map

         3mm                              3mm × 3cm/4cm = 2.25mm

         4mm                               4mm × 3cm/4cm = 3mm

         5mm                               5mm × 3cm/4cm = 3.75mm

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