Question

The figures below are similar.

Answer 1

Answer:  The correct option is (B) $\dfrac{7}{2}~\textup{and}~\dfrac{49}{4}.$

Step-by-step explanation:  We are given to find the ratio of the perimeters and the ratio of the areas of the larger figure to the smaller figure in the picture.

The SIMILARITY ratio of two figures is given by the ratio of the length of a side of the first figure to the length of the corresponding side of the second figure.

Therefore, similarity ratio of the given figures is

$S_r=\dfrac{\textup{length of a side of the larger figure}}{\textup{length of the corresponding side of the smaller figure}}\\\\\\\Rightarrow S_r=\dfrac{28}{8}\\\\\\\Rightarrow S_r=\dfrac{7}{2}.$

(a) We know that the ratio of the perimeters of two similar figures is equal to the similarity ratio of the figures.

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

$P_r=\dfrac{7}{2}.$

(b) We know that the ratio of the areas of two similar figures is equal to the ratio of the square of the length of a side of the first figure to the square of the length of the corresponding side of the second figure.

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

$A_r=\dfrac{28^2}{4^2}\\\\\\\Rightarrow A_r=\dfrac{49}{4}.$

Thus, the required ratios are $\dfrac{7}{2}~\textup{and}~\dfrac{49}{4}.$

Option (B) is CORRECT.

Answer 2

I believe the answer is B :-)