Question

How do i find scale factor from the smaller figure to the larger?

Answer 1

Consider that the scale factor of a new figure to the initial figure, given that both figures are similar, is given by the ratio of their respective corresponding dimensions,

`SF=\frac{\text{ Dimension in final figure}}{\text{ Corresponding dimension in initial figure}}`

It is asked to consider the smaller figure as the initial figure and the larger figure as the final figure.

1.

Consider that the dimension measuring 21 units in the final (left side) diagram, measures 7 units in the initial (right side) diagram. So the associated scale factor is calculated as,

`\begin{gathered} SF=(21)/(7) \\ SF=(3\cdot7)/(7) \\ SF=3 \end{gathered}`

Thus, the required scale factor is,

`3`

2.

Consider that the side measuring 8 units in the final (left side) diagram, measures 4 units in the initialtia (right side) diagram. So the associated scale factor is calculated as,

`\begin{gathered} SF=(4)/(8) \\ SF=(4)/(4\cdot2) \\ SF=(1)/(2) \end{gathered}`

Thus, the required scale factor is obtained as,

`(1)/(2)`