Finding equivalent ratios in similar triangles | Grade 8 (TX) | Khan Academy

We're told Triangle FGH is similar to Triangle KLM. Which proportion could we use to find the length of segment KL? So segment KL is this one right over here, and they put an X there for the length of segment KL. Pause this video and see if you can figure it out.

And I know it's a little awkward; I put the choices up here just so it would all fit into one window without having to scroll. But pause this video and see which choice you would pick.

All right, now let's work through this together.

All right, so before I even look at the choices, it might be useful for me to think about what is the corresponding side to KL. Just eyeballing it, it looks like it is side FG. But I want to make sure because what we could look at is just even how they've defined the triangles or how they've written them. FG are the first two listed, and KL are the first two listed. So actually, this makes me confident that side FG corresponds to KL and these are both similar.

So now let's think about what these are, what all of these are doing over here.

So this first choice, it's comparing X to 168. So it looks like it's looking at the ratio of the length of this side of KL to LM. So X over 168, so that should be the same ratio as... and let's see, 168 is the longest side of this triangle. So that should correspond to this one right over here.

So X over 168 should be the same thing as 58 over 112. That is not what they wrote; they wrote 112 over 58, so I am going to rule this one out.

Now, when we go to the second choice, this is looking pretty good. X over 168, X over 168... well, that should be equivalent to the ratio of the corresponding sides in that same order in the other triangle. X over 168 corresponds to the X that should be the 58, corresponding to the 168, which should be the 112. So that should be equal to 58 over 112, which is exactly what this choice is.

So we're really done, but let me just look at these other ones, make sure that these aren't correct, even though I think there's only one choice here. 58 over X, so that's the ratio of this to this, and then they're saying that's the ratio of 112. That should be the ratio of 112 to 168, so if this had a 168 here, that would have been right.

And then they're saying 58 over X, so the ratio of this to this is equivalent to the ratio of 141 over 112, which, once again, that's strange on a lot of levels. So yes, I like Choice B here.