Questions: In the similar images below, what are the missing perimeter and area? P=30 A=? P=? A=27

In the similar images below, what are the missing perimeter and area? P=30 A=? P=? A=27
Transcript text: In the similar images below, what are the missing perimeter and area? $P=30$ $A=$ ? $P=$ ? $A=27$
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Solution

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Solution Steps

Step 1: Find the scale factor

The ratio of corresponding sides in similar figures is the scale factor. In this case, the side lengths are 6 and 9. The scale factor is 9/6 = 1.5 (larger figure to smaller figure).

Step 2: Find the missing perimeter

Since the figures are similar, the ratio of their perimeters is equal to the scale factor. Let the missing perimeter be P. We have P/30 = 1.5. Therefore, P = 30 * 1.5 = 45.

Step 3: Find the missing area

The ratio of the areas of two similar figures is equal to the square of the scale factor. Let the missing area be A. We have 27/A = (1.5)^2 = 2.25. Therefore, A = 27/2.25 = 12.

Final Answer

P = 45 A = 12

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