Question

ΔABC is similar to ΔAXY by a ratio of 4:3. If BC = 24, what is the length of XY?

triangles ABC and AXY that share vertex A where point X is between points A and B and point Y is between points A and C

Answer 1

These are the answer choices:
XY = 18
XY = 32
XY = 6
XY = 8

Answer 2

If \(\triangle ABC\) is similar to \(\triangle AXY\) by a ratio of \(4:3\), what can you say about the ratio of the lenghts of \(BC\) and \(XY\)?

Answer 3

I am not really sure. I don't do good with ratios

Answer 4

The upshot here is that if the triangles are similar by a given ratio, then their corresponding lengths are also related by that same ratio. In this case, this means that we have the following relation:
\[\dfrac{BC}{XY} = \dfrac{4}{3}.\]
Now all you need to do is solve for \(XY\), since \(BC\) is given.

Answer 5

can you explain how I do that? Again, not good with ratios

Answer 6

Well, I think the easiest way is to take the reciprocal of both sides of the equality:
\(\dfrac{BC}{XY} = \dfrac{4}{3} \iff \dfrac{XY}{BC} = \dfrac{3}{4}.\)

Now multiply both sides by \(BC\):
\(XY= \dfrac{3}{4}BC.\)

All you need to do now is substitute \(BC = 24\) and you are done.

Answer 7

Thanks!