Determine 𝐴𝐵 over 𝐵𝐷, if 𝐴𝐷 over 𝐷𝐵 is equal to 38 over 23.
In this question, we need to find the ratio of the lengths 𝐴𝐵 to 𝐵𝐷. We’re told that the ratio of 𝐴𝐷 to 𝐷𝐵 is 38 to 23. We can therefore say that 𝐴𝐷 has length 38 units. And 𝐷𝐵 has length 23 units. This is shown on the diagram in orange and pink. The length 𝐴𝐵 is the length 𝐴𝐷 plus the length 𝐷𝐵. We can therefore calculate the length of 𝐴𝐵 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. 𝐴𝐷 is 38. 𝐷𝐵 is 23. And 𝐴𝐵 is 61. The length 𝐵𝐷 is the same as the length 𝐷𝐵. This means that 𝐵𝐷 is equal to 23.
We can therefore conclude that the ratio 𝐴𝐵 to 𝐵𝐷 is 61 to 23. If 𝐴𝐷 over 𝐷𝐵 is equal to 38 over 23, then 𝐴𝐵 over 𝐵𝐷 is equal to 61 over 23.