Video Transcript
What is the ratio between lengths
𝐴𝐶 and 𝐴𝐸 in its simplest form?
Our ratio here will be a comparison
of lengths. The first segment we’re interested
in is 𝐴𝐶, which is this distance. And the second distance we’re
interested in is 𝐴𝐸, which is this distance. Before we do anything else, we
should note that our ratio is going to be 𝐴𝐶 to 𝐴𝐸. This is because when our ratio is
listed, 𝐴𝐶 came first and 𝐴𝐸 came second. And that determines the order of
our ratio. But when we look closer at the line
segment, we realize that we’re not given any exact distances.
But we are told that each of these
segments are equal in length. And 𝐴𝐶 contains two of those
equal segments, while 𝐴𝐸 contains four of those equal segments. And that means we could list a
ratio as two to four. If you’re still not sure that this
is true because we don’t have a measurement, imagine that the length of segment 𝐴𝐵
was five inches. That would mean each of these
segments was five inches. That would make 𝐴𝐶 10 inches and
𝐴𝐸 20 inches. That would be an equivalent
ratio. The ratio of the side lengths will
be two to four no matter how we’re measuring the distance.
However, we’ve 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 𝐴𝐶 to 𝐴𝐸 is one to
two. If you want one more way to
visualize this, for every one segment on 𝐴𝐶, there are two segments on 𝐴𝐸. Again, we can find one segment on
𝐴𝐶 and two segments on 𝐴𝐸, a ratio of one to two.
