Question Video: Finding the Ratio between Two Line Segments in the Simplest Form | Nagwa Question Video: Finding the Ratio between Two Line Segments in the Simplest Form | Nagwa

Question Video: Finding the Ratio between Two Line Segments in the Simplest Form Mathematics

What is the ratio between lengths ๐ด๐ถ and ๐ด๐ธ in its simplest form?

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Video Transcript

What is the ratio between lengths ๐ด๐ถ and ๐ด๐ธ in its simplest form?

Our ratio here will be a comparison of lengths. The first segment weโre interested in is ๐ด๐ถ, which is this distance. And the second distance weโre interested in is ๐ด๐ธ, which is this distance. Before we do anything else, we should note that our ratio is going to be ๐ด๐ถ to ๐ด๐ธ. This is because when our ratio is listed, ๐ด๐ถ came first and ๐ด๐ธ came second. And that determines the order of our ratio. But when we look closer at the line segment, we realize that weโre not given any exact distances.

But we are told that each of these segments are equal in length. And ๐ด๐ถ contains two of those equal segments, while ๐ด๐ธ contains four of those equal segments. And that means we could list a ratio as two to four. If youโre still not sure that this is true because we donโt have a measurement, imagine that the length of segment ๐ด๐ต was five inches. That would mean each of these segments was five inches. That would make ๐ด๐ถ 10 inches and ๐ด๐ธ 20 inches. That would be an equivalent ratio. The ratio of the side lengths will be two to four no matter how weโre measuring the distance.

However, weโ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 ๐ด๐ถ to ๐ด๐ธ is one to two. If you want one more way to visualize this, for every one segment on ๐ด๐ถ, there are two segments on ๐ด๐ธ. Again, we can find one segment on ๐ด๐ถ and two segments on ๐ด๐ธ, a ratio of one to two.

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