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

In a figure, segments π‘‹π‘Œ and 𝐡𝐢 are parallel. If 𝐴𝑋 = 18, 𝑋𝐡 = 24, and π΄π‘Œ = 27, what is the length of line segment π‘ŒπΆ?


Video Transcript

In the figure, the sides π‘‹π‘Œ and 𝐡𝐢 are parallel. If 𝐴𝑋 equals 18, 𝑋𝐡 equals 24, and π΄π‘Œ equals 27, what is the length of π‘ŒπΆ?

We’re given the side lengths 𝐴𝑋, 𝑋𝐡, and π΄π‘Œ. And we want to find the length of π‘ŒπΆ. We’re also told that the sides π‘‹π‘Œ and 𝐡𝐢 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‘Œ is to π‘ŒπΆ as 𝐴𝑋 is to 𝑋𝐡. Now, if we substitute our known lengths into this equation, π΄π‘Œ is 27, 𝐴𝑋 is 18, and 𝑋𝐡 is 24, we have 27 over π‘ŒπΆ is equal to 18 over 24. We can rearrange this to get π‘Œπ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‘ŒπΆ is 36 units.

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