### Video Transcript

Segment πΆπ· has mirror symmetry in
the line π΄πΉ. Given that πΈπ· is equal to five
and π΅πΆ is equal to 5.1, calculate the perimeters of π΄πΆπΉπ· and triangle
π΅πΆπ·.

As the line π΄πΉ is a line of
symmetry, we know that the lengths of several sides will be equal. The length π΄πΆ will be equal to
the length π΄π·. Both of these have length 6.7. The lengths π΅πΆ and π΅π· are also
equal in length. We are told that π΅πΆ is equal to
5.1. Therefore, π΅π· is also equal to
5.1. The lengths πΈπ· and πΈπΆ are also
equal in length. πΈπ· is equal to five. Therefore, πΈπΆ is also equal to
five. Finally, the lengths π·πΉ and πΆπΉ
are also equal. Weβre told in the diagram that πΆπΉ
is equal to 8.2. Therefore, π·πΉ is also equal to
8.2.

The first perimeter weβre asked to
calculate is that of π΄πΆπΉπ·. This is the outside of the
shape. We can calculate this by adding the
four lengths π΄πΆ, πΆπΉ, πΉπ· and π·π΄. π΄πΆ and π΄π· or π·π΄ are both
equal to 6.7. πΆπΉ and πΉπ· or π·πΉ are both
equal to 8.2. We need to add 6.7, 8.2, 8.2, and
6.7. 6.7 plus 8.2 is equal to 14.9. This means that 8.2 plus 6.7 is
also equal to 14.9. 14.9 plus 14.9 or two times 14.9 is
equal to 29.8. The perimeter of π΄πΆπΉπ· is
29.8.

We also need to calculate the
perimeter of the triangle π΅πΆπ·. This is equal to the three lengths
π΅πΆ, πΆπ· and π·π΅. This can be split into four lengths
that we know, π΅πΆ, πΆπΈ, πΈπ· and π·π΅. π΅πΆ and π΅π· are both equal to
5.1. πΆπΈ and πΈπ· are both equal to
five. We need to add 5.1, five, five, and
5.1. 5.1 plus five is equal to 10.1. We get the same answer when we add
them the other way round. 10.1 plus 10.1 is equal to
20.2. The perimeter of triangle π΅πΆπ· is
20.2. Therefore, our two correct answers
are 29.8 and 20.2.