Here's introductory information on compound forms, which is what 늘어나다 is. You ask about 어나라, but it is actually 늘어 + 나다, a compound word made up of 늘다 and 나다. 나다 has many meanings, but they are all related to "out". It is working as a helper verb here by attaching to others. So 늘어나다 is one example of the common [V1 + 아/어] + V2 compound form, where V2 is an auxiliary(helper) verb. -아/어 is a verb connective form which can make a loose or tight connection to form a new expression or word. For example, 밝아 오다 is a loose connection while 밝아지다 and 돌아오다 are tight ones making brand new words. This kind of new expressions and words are probably the most common way new vocabulary is made in Korean. So it is worthwhile to have a good understanding of such constructions. Here are some examples: (나다<->들다 aux. verb examples) - 늘다(increase, improve) + 나다(come out, exit) => 늘어나다(increase, expand, stretch). - 벗다(take off, shed) + 나다 => 벗어나다 => free oneself, get out of something undesirable. - 일다(form, rise, make ripples) + 나다 => 일어나다(come about, happen). - 줄다(decrease, shrink) + 들다(come in, inward) => 줄어들다(decrease, shrink) - 덤비다(take on, challenge) + 들다 => 덤벼들다 => come at someone; pounce on someone. (오르다<->내리다, 가다<->오다 examples) - 오르다(rise, go up) + 가다(go) => 올라가다(go up, climb). - 내리다(fall, come down) + 오다(come) => 내려오다(come down, descend). (examples with 하다) - 하다(do) + 내다(bring out - causative of 나다) => 해내다(complete something, win against someone/something) - 하다(do) + 주다(do for someone, give) => 해 주다(do something for someone) - not a word in itself. - 하다(do) + 놓다(put, leave) => 해 놓다(do something and leave it in place - for some purpose) - 하다(do) + 두다(put, store) => 해 두다(do something (in case it might be needed)). - 하다(do) + 버리다(be done with something) => 해 버리다(be done with something for good). - 하다(do) + 치우다(put it aside) => 해 치우다(finish something to get out of the way).

늘어나라 is the imperative version of 늘어나다. 늘다 and 늘어나다 are two different verbs, albeit similar to some degree. 늘다: to get improved, to increase, to be extended 늘어나다: to stretch, to increase you could replace 늘어나라 with 늘어라, but 늘어나라 is clearly the better pick since you want a visible/considerable increase. Further, 늘어라 can be easily mistaken for "get improved", and it indirectly sets a maximum on how far it shall increase. which is undesirable. Korean really isn't an easy language, I realize again and again....