The equation for the area of a triangle is A= b*h /2. So, plug in your known variables, and you get 270in^2= b*30 /2. First you multiply by 2 to cancel out the division for 2, which gets you 540= b* 30. To get "b" by itself, divide both sides by 30, giving you 18=b.
To check this, plug in your new known variable, as 270= 18* 30 /2. This will equal as 270=270, confirming 18in as the correct measurement.