Yale has a square-shaped garage with 228 square feet of floor space. she plans to build an addition that will increase the floor space by 50%. what will be the length, to the nearest tenth, of one side of the new garage?

So yale has a total of 228 square feet and he wants to increase it by 50% meaning you're going to add the half off 228 to 228 makes sense?
228 is 100%
228÷2 =114 which is 50%
228 + 114 = 342 
342 is the new space now because its a square the formula for the area l×w but since in a square all sides are equal you just pick a side ( x ) and square it so it'll be x² 
but since you already have the area you're going to do the opposite of squaring and square root instead so: 
√342 =18.493242.. ≈ 18.5
18.5 is your answer i hope this helps