The area of a triangle is hb/2, we are told the base but not the side lengths. The side length can be found using the pythagorean theorem.
s^2=(b/2)^2+h^2
The height can be found from the area because:
A=bh/2 so
h=2A/b then our pythagorean identity becomes:
s^2=(b/2)^2+(2A/b)^2
s^2=b^2/4+4A^2/b^2 or a little more neatly
s^2=(b^4+15A^2)/(4b^2), we were told A=150 and b=12 so
s^2=358236/576
s=√(358236/576) ft
s≈24.939 to nearest thousandth (which means that they actually rounded wrong because that's...
s≈24.9 to nearest tenth (they must have made earlier rounding somewhere in the earlier calculations, that's why you use symbols until the final calculation :P)
Anyway, they rounded to 25.0