### Video Transcript

Given that π΄π΅πΆπ· is similar to
ππππΏ and the perimeter of π΄π΅πΆπ· is 66.2 centimeters, calculate the perimeter
of ππππΏ, giving your answer to two decimal places.

Weβre told that polygons π΄π΅πΆπ·
and ππππΏ are similar, which means that two key things are true. Firstly corresponding angles are
congruent, and secondly corresponding sides are proportional. Here, weβre asked about the
perimeter of ππππΏ. So this second property is going to
be useful.

As the perimeter is simply the sum
of the side lengths, the perimeters of similar polygons are in the same proportion
as the corresponding side lengths themselves. As weβve been given the perimeter
of π΄π΅πΆπ·, we can calculate the perimeter of ππππΏ if we know what this
proportion is. To work this out, letβs see if we
can identify a pair of corresponding sides on the two polygons whose lengths we
know.

The ordering of the letters in the
similarity statement is important, because it reveals which vertices in the two
shapes are corresponding. Vertex π΄ corresponds with vertex
π, vertex π΅ corresponds with vertex π, and so on. We can identify that side π΅πΆ is
corresponding with side ππ. And weβve been given the lengths of
both of these sides. π΅πΆ is 16 centimeters, and ππ is
10 centimeters.

We can then write down the
proportion. And as itβs the perimeter of
ππππΏ that we want to calculate later, weβll use lengths from this polygon in the
numerator of the fraction. We have ππ over π΅πΆ is equal to
10 over 16. This fraction can be simplified to
five over eight.

We can now form an equation using
the perimeters of the two polygons. As theyβre in the same proportion
as the individual side lengths, we have that the perimeter of ππππΏ over the
perimeter of π΄π΅πΆπ· is equal to five over eight. We can then substitute 66.2 for the
perimeter of π΄π΅πΆπ·. To solve this equation, we multiply
both sides by 66.2 and then evaluate. This gives 331 over eight, which is
41.375.

The question specifies that we
should give our answer to two decimal places. So, rounding as required and
including the units, weβve found that the perimeter of polygon ππππΏ is 41.38
centimeters to two decimal places.