Question

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?

Answer 1

The smallest possible length of congruent sides of an acute isosceles triangle must be  <  than the length of congruent sides of the right isosceles triangle

so 
The sides of a right isosceles triangle are in proportion: √2/2:√2/2:1

if  the longest side of an acute isosceles triangle is ----------- > 8 centimeters 
then
the smallest possible length of one of the two congruent sides
is 8*√2/2- ---------->4√2=5.66=5.6
5.6<5.66------------- is ok

we know that the two smallest sides of a triangle have to add up to be longer than the longest side.

2x>8---------- > x>4
therefore the solution is the interval (4,5.6)
the smallest possible length rounded to the nearest tenth is 4.1

the answer is 4.1