### Video Transcript

Find the value of π₯.

When we look at our diagram, we see
a larger triangle that is cut by the segment π·πΈ. And this line segment π·πΈ is
parallel to one of the side lengths π΅πΆ. And when a triangle is cut by a
line segment thatβs parallel to one of its side lengths, two similar triangles are
created. So we can say that if weβre given
line segment π·πΈ is parallel to π΅πΆ, the smaller triangle, triangle π΄π·πΈ, is
similar to the larger triangle, triangle π΄π΅πΆ. So we can say that π΄π· over π΄π΅
is equal to π·πΈ over π΅πΆ. This is because in similar
triangles corresponding side lengths are proportional.

Side length π΄π· measures 10, but
what about π΄π΅? And this is where we need to be
very careful. Side length π΄π΅ is not equal to
11. Side length π΄π΅ is the full
distance from vertex π΄ to vertex π΅, which is 21. So π΄π· over π΄π΅ will be equal to
10 over 21. We know that side length π·πΈ is
equal to 10 as well. So we now have a proportion that
says 10 over 21 is equal to 10 over π΅πΆ. And that means π΅πΆ must be equal
to 21 so that these side lengths stay in proportion. Since side length π΅πΆ equals 21,
our missing π₯-value is 21.