Answer:
The smallest possible length would be 8.5 cm.
Step-by-step explanation:
Since, an acute isosceles triangle having two congruent sides with three acute interior angles,
Given,
The longest side of an acute isosceles triangle is 12 centimeters,
Let x be the side length of the each of the congruent sides,
So, by the property of acute isosceles triangle,
\(x^2+x^2\geq (12)^2\)
\(2x^2\geq 144\)
\(x^2\geq 72\)
\(\implies x\geq \sqrt{72}=8.48528137424\approx 8.5\)
Hence, the smallest possible length of one of the two congruent sides is 8.5 cm
