Question

The figures below are similar.

(picture attached below)

What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.

Answer Choices:

A. 8/3 and 49/4
B. 7/2 and 49/4
C. 7/2 and 9/4
D. 8/3 and 9/4

This is so confusing!! :( How are you supposed to calculate perimeter if you're given some kind of contorted figure and only the measure of the base?!?

For real, though. This is why I hate math -_-

Thank you so much in advance! :) If you could explain how I can solve this problem, it would be more appreciated than simply giving me the answer (because you can't learn from being handed answers and no explanation to solve it yourself).

Answer 1

I believe the answer is B :-)

Answer 2

Answer: The correct option is (B)
`(7)/(2)~\textup{and}~(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=\frac{\textup{length of a side of the larger figure}}{\textup{length of the corresponding side of the smaller figure}}\\\\\\\Rightarrow S_r=(28)/(8)\\\\\\\Rightarrow S_r=(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=(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=(28^2)/(4^2)\\\\\\\Rightarrow A_r=(49)/(4).`

Thus, the required ratios are
`(7)/(2)~\textup{and}~(49)/(4).`

Option (B) is CORRECT.