Video: Finding the Length of a Side in a Triangle Using the Relation between Parallel Lines

Determine 𝐴𝐡/𝐡𝐷, if 𝐴𝐷/𝐷𝐡 = 38/23.

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Video Transcript

Determine 𝐴𝐡 over 𝐡𝐷, if 𝐴𝐷 over 𝐷𝐡 is equal to 38 over 23.

In this question, we need to find the ratio of the lengths 𝐴𝐡 to 𝐡𝐷. We’re told that the ratio of 𝐴𝐷 to 𝐷𝐡 is 38 to 23. We can therefore say that 𝐴𝐷 has length 38 units. And 𝐷𝐡 has length 23 units. This is shown on the diagram in orange and pink. The length 𝐴𝐡 is the length 𝐴𝐷 plus the length 𝐷𝐡. We can therefore calculate the length of 𝐴𝐡 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. 𝐷𝐡 is 23. And 𝐴𝐡 is 61. The length 𝐡𝐷 is the same as the length 𝐷𝐡. This means that 𝐡𝐷 is equal to 23.

We can therefore conclude that the ratio 𝐴𝐡 to 𝐡𝐷 is 61 to 23. If 𝐴𝐷 over 𝐷𝐡 is equal to 38 over 23, then 𝐴𝐡 over 𝐡𝐷 is equal to 61 over 23.

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