Complete Question:
Johnny printed two maps of a walking trail near his home. The length of the walking trail on the first map is 8 cm.
(a) Choose a length between 5 cm and 15 cm for the walking trail on the second map: ________cm.
(b) Determine the scale factor from the first map to the second map.
(c) A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the triangle landmark on the second map?
(d) Draw one of the triangles from part C. Label the side lengths and vertices accordingly. You may use this drawing tool or draw your triangle on paper:
Answer:
(a) Length = 4cm
(b) Scale factor = 0.5
(c) 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale
(d) See attachment for triangle
Step-by-step explanation:
(a) Choose a length between 5 cm and 15 cm
[tex]Length =4cm[/tex] --- This is solely up to you (you can make use of any length between 5 cm and 15 cm)
(b) The scale factor
The scale factor (k) is calculated as:
[tex]k = \frac{New\ Length}{Old\ Length}[/tex]
[tex]k = \frac{4cm}{8cm}\\[/tex]
[tex]k = 0.5[/tex]
(c) What are side lengths of 3 cm, 4 cm, and 5 cm on the second landmark
Using:
[tex]k = \frac{New\ Length}{Old\ Length}[/tex]
The old lengths, in this case are: 3cm, 4cm and 5cm
Make New length the subject
[tex]New\ Length = k * Old\ Length[/tex]
When [tex]Length = 3cm[/tex]
[tex]New\ Length = 0.5 * 3cm = 1.5cm[/tex]
When [tex]Length = 4cm[/tex]
[tex]New\ Length = 0.5 * 4cm = 2cm[/tex]
When [tex]Length = 5cm[/tex]
[tex]New\ Length = 0.5 * 5cm = 2.5cm[/tex]
So: 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale
(d) See attachment for triangle
