In triangle ABC point D is on AB and point E is on BC such that DE If DB = 4, DA = 14 and DE = 6 what is AC

It is important to make a drawing of what they are telling you.

Once you have your drawing, its a matter of setting up the ratio of the smaller triangle's sides to the larger triangle.

Bigger triangle is ABC, where AB = AD + DB ==> 14 + 4 = 18

Smaller triangle is DBE, where DB = 4, and DE = 6.

Now side AB corresponds to side DB, and side AC corresponds to side DE.

We set up the ratio as follows:

AB/DB = AC/DE ===> 18/4 = AC/6.

Cross multiplication will give us the following:

18 * 6 = AC * 4

108 = 4AC , we now divide both sides by 4, and AC = 27.