Question Video: Finding the Unknown Lengths in a Triangle given the Other Sidesβ Lengths Using the Relations of Parallel Lines Mathematics • 11th Grade

In a figure, segments ππ and π΅πΆ are parallel. If π΄π = 18, ππ΅ = 24, and π΄π = 27, what is the length of line segment ππΆ?

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Video Transcript

In the figure, the sides ππ and π΅πΆ are parallel. If π΄π equals 18, ππ΅ equals 24, and π΄π equals 27, what is the length of ππΆ?

Weβre given the side lengths π΄π, ππ΅, and π΄π. And we want to find the length of ππΆ. Weβre also told that the sides ππ and π΅πΆ are parallel. Now, the side splitter theorem tells us that if a line parallel to one side of a triangle intersects the other two sides, then that line divides those two sides proportionally. In particular, in our case this means that π΄π is to ππΆ as π΄π is to ππ΅. Now, if we substitute our known lengths into this equation, π΄π is 27, π΄π is 18, and ππ΅ is 24, we have 27 over ππΆ is equal to 18 over 24. We can rearrange this to get ππΆ equal to 24 over 18 times 27, which evaluates to 36.

And so using the side splitter theorem, we find that the length of ππΆ is 36 units.