The longest side of an acute isosceles triangle is 8 centimeters. rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides

-- If the two congruent sides are any shorter than 4 cm, then
they can't reach end-to-end on the 8-cm side.

-- If they're exactly 4 cm, then they lie right on top of the 8 cm side,
and the triangle looks like a line segment that's 8 cm long.

-- The two congruent sides must be more than 4 centimeters long.

There's no such thing as their "smallest possible length".  It can be
anything, just as long as it's more than 4 cm. 

Whatever length that you name, no matter how close it is to 4 cm,
I can always name a shorter length that's still more than 4 cm.

So when it's rounded to the nearest tenth, hundredth, thousandth,
millionth etc., it's 4 cm. 

She will need 5/8 bags for each square yard.