The smallest possible length of one of the two congruent sides is 5.7 cm and this can be determined by using the Pythagorean theorem for an acute triangle.
Given :
The longest side of an acute isosceles triangle is 8 centimeters.
The following steps can be used in order to determine the smallest possible length of one of the two congruent sides:
Step 1 - The Pythagorean theorem for an acute triangle can be used in order to determine the smallest possible length of one of the two congruent sides.
Step 2 - Let the length of the smaller sides be 'a' and let the length of the larger side be 'b'.
Step 3 - According to the Pythagorean theorem for an acute triangle:
[tex]\rm H^2 < B^2+P^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 4 - Substitute the values of the known terms in the above expression.
[tex]a^2+a^2>b^2[/tex]
[tex]2a^2>b^2[/tex]
Step 5 - Substitute the value of x in the above expression.
[tex]2a^2>8^2[/tex]
a > [tex]\sqrt{32}[/tex]
a > 5.6
Therefore, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/22568405
