### Video Transcript

Determine π΄π΅ over π΅π·, if π΄π· over π·π΅ is equal to 38 over 23.

In this question, we need to find the ratio of the lengths π΄π΅ to π΅π·. Weβre told that the ratio of π΄π· to π·π΅ is 38 to 23. We can therefore say that π΄π· has length 38 units. And π·π΅ has length 23 units. This is shown on the diagram in orange and pink. The length π΄π΅ is the length π΄π· plus the length π·π΅. We can therefore calculate the length of π΄π΅ by adding 38 and 23. 30 plus 20 is equal to 50. And eight plus three is equal to 11. Therefore, 38 plus 23 equals 61. We now have three lengths on the triangle. π΄π· is 38. π·π΅ is 23. And π΄π΅ is 61. The length π΅π· is the same as the length π·π΅. This means that π΅π· is equal to 23.

We can therefore conclude that the ratio π΄π΅ to π΅π· is 61 to 23. If π΄π· over π·π΅ is equal to 38 over 23, then π΄π΅ over π΅π· is equal to 61 over 23.