# Video: Using the Similarity between Two Shapes to Find the Scale Factor of One Shape to the Other and the Perimeter of One of Them

If π΄π΅πΆπ·πΈ ~ πππππ, Find the scale factor of π΄π΅πΆπ·πΈ to πππππ and the perimeter of πππππ.

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### Video Transcript

If the pentagon π΄π΅πΆπ·πΈ is similar to the pentagon πππππ. Find the scale factor of π΄π΅πΆπ·πΈ to πππππ and the perimeter of πππππ.

In order to calculate the scale factor, we need to find corresponding sides of the two pentagons. In this case, πΆπ· is equal to 21 and ππ is equal to 14. This means that the scale factor will be 21 divided by 14. This can be simplified to three over two or 1.5 as a decimal. This means that the larger pentagon has length 1.5 times as long as the smaller pentagon.

The perimeter of any shape is the total distance around the outside of the shape. In this example, we can work out the perimeter of pentagon π΄π΅πΆπ·πΈ by adding 24, 24, 21, 21, and 27. This is because length π΅πΆ is the same as length π΄π΅. In the same way, length πΆπ· is the same as length π΄πΈ. Adding these numbers gives us the perimeter of the larger pentagon of 117.

To calculate the perimeter of the smaller pentagon, we need to divide this answer 117 by the scale factor β in this case 1.5 or three over two. 117 divided by 1.5 is equal to 78. This means that the perimeter of the smaller pentagon is 78.

We could also have worked out the perimeter of the smaller pentagon by working out each individual length β the length of ππ, ππ, ππ, and ππ. This could be done by dividing the corresponding length in the larger pentagon by 1.5. Adding these numbers β 16, 16, 14, 18, and 14 β also gives us an answer of 78.