the longest side of an acute isosceles triangle is 12 centimeters. rounded to the nearest tenth, what is the…

Explanation:

Step1: Use the property of an acute isosceles triangle

For an acute isosceles triangle with the longest side (c = 12) and the congruent sides (a=b). By the Pythagorean - like condition for an acute triangle (a^{2}+a^{2}>c^{2}) (using the fact that if (a = b), and the triangle is acute, the sum of the squares of the two equal sides is greater than the square of the longest side).

Step2: Substitute (c = 12) into the inequality

We have (2a^{2}>12^{2}), which simplifies to (2a^{2}>144). Then (a^{2}>72), and (a>\sqrt{72}).

Step3: Calculate (\sqrt{72})

(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\approx6\times1.414 = 8.484)

Answer:

(8.5\mathrm{cm})