Question

Triangles ABC and LMN are given such that



AB = 24, BC = 20, and AC = 40

LM = 6, MN = 5, and LN = (3a + 1)




To be similar, which should be the value of a?

Answer 6
5
4
3

Answer 1

If ABC and LMN are similar, then basically one is a "blown up" version of the other. We have to match up the sides so that there is a single number we can multiply the lengths by to get the other set. For example, LM = 6 and AB = 24, so if we multiply LM by 4, we get 24.

Also, 5*4 = 20, so 4 works for MN and BC. To get LN and AC to match up, then, we have to multiply LN by 4 to get 40. We get
\[4(3a+1) = 40\]which has the solution a = 3.