Question

If triangle LMN is similar to triangle RST with LM = 3, MN = 4, and ST = 12, what is the length of RS in triangle RST?

Answer 1

16

Explanation:

If triangle LMN is similar to triangle RST, it means that the corresponding sides of the two triangles are proportional. In other words, the ratio of the lengths of corresponding sides in the two triangles is the same.

Let's denote the length of RS as x. Then, we can set up a proportion based on the given information:

`(LM)/(ST) = (MN)/(RS)`

Substituting the values we have:

`(3)/(12) = (4)/(x)`

Now, we can cross-multiply and solve for x:

`3x = 12 \cdot 4`

`3x = 48`

Now, divide both sides by 3 to solve for x:

`x = (48)/(3)`

`x = 16`

So, the length of RS in triangle RST is 16 units.