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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

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1 Answer

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.