### Video Transcript

What is the ratio between lengths
๐ด๐ถ and ๐ด๐ธ in its simplest form?

Our ratio here will be a comparison
of lengths. The first segment weโre interested
in is ๐ด๐ถ, which is this distance. And the second distance weโre
interested in is ๐ด๐ธ, which is this distance. Before we do anything else, we
should note that our ratio is going to be ๐ด๐ถ to ๐ด๐ธ. This is because when our ratio is
listed, ๐ด๐ถ came first and ๐ด๐ธ came second. And that determines the order of
our ratio. But when we look closer at the line
segment, we realize that weโre not given any exact distances.

But we are told that each of these
segments are equal in length. And ๐ด๐ถ contains two of those
equal segments, while ๐ด๐ธ contains four of those equal segments. And that means we could list a
ratio as two to four. If youโre still not sure that this
is true because we donโt have a measurement, imagine that the length of segment ๐ด๐ต
was five inches. That would mean each of these
segments was five inches. That would make ๐ด๐ถ 10 inches and
๐ด๐ธ 20 inches. That would be an equivalent
ratio. The ratio of the side lengths will
be two to four no matter how weโre measuring the distance.

However, weโve been told that we
want the simplest form. And that means we need to consider
if two and four share any common factors. Both of these values are divisible
by two. Two divided by two is one. Four divided by two is two. And that means, in simplest form,
the ratio of these side lengths would be one to two. The ratio of ๐ด๐ถ to ๐ด๐ธ is one to
two. If you want one more way to
visualize this, for every one segment on ๐ด๐ถ, there are two segments on ๐ด๐ธ. Again, we can find one segment on
๐ด๐ถ and two segments on ๐ด๐ธ, a ratio of one to two.