Question

Write the scale factors and values for x for the pairs of similar triangles below. 3. 2. E B 8 cm 9 cm D B' 5 cm F x cm A Kcm 4 cm A 2 cm с Di CH 7.5 cm Scale Factor Scale Factor:

Answer 1

The scale factor is the ratio between equivalent sides and is the same for any pairs of sides, so:

For exercise 1:

`\begin{gathered} scalefactor=(A^(\prime)B^(\prime))/(AB)=(A^(\prime)C^(\prime))/(AC)=(2)/(4)=(1)/(2)=0.5 \\ (x)/(9)=(2)/(4) \\ x=(2)/(4)\cdot9 \\ x=(9)/(2)=4.5 \\ \end{gathered}`

The scale factor is 1/2 = 0.5 and x = 9/2 = 4.5.

For exercise 2:

`\begin{gathered} \text{scale factor=}(E^(\prime)F^(\prime))/(EF)=(F^(\prime)D^(\prime))/(FD)=(7.5)/(5)=1.5 \\ (x)/(8)=1.5 \\ x=1.5\cdot8 \\ x=12 \end{gathered}`

The scale factor is 1.5 and x = 12