Question

10) What is the ratio of areas ofthe smaller figure to the largerfigure?

Answer 1

The corresponding widths of the smaller and larger figures are given as 2cm and 3cm respectively,

Hence, the ratio of their widths/sides is determined as:

`\begin{gathered} \frac{\text{ width of smaller figure}}{\text{width of larger figure}}=(2)/(3), \\ \text{Therefore, scale factor =}(2)/(3) \end{gathered}`

The ratio of their areas of the smaller to the larger figure is the square of the scale factor

`\text{ Area factor =(}(2)/(3))^2=(4)/(9)`

Therefore, the ratio of the areas of the smaller figure to the larger figure is

`(4)/(9)`