The longest side of an acute isosceles triangle is 12 centimeters. rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
6.0 cm
6.1 cm
8.4 cm
8.5 cm

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

An isosceles triangle is a triangle with two equal sides and two equal angles

Let

x------> the possible length of one of the two congruent sides

Applying the triangle inequality theorem

solve for x

therefore

the answer is

The smallest possible length of one of the two congruent sides rounded to the nearest tenth is 6.1 cm and it can be determine by using triangle inequality theorem.

Given :

The longest side of an acute isosceles triangle is 12 centimeters.

According to the triangle inequality theorem, the third side of the triangle is less than the sum of the other two sides of the triangle.

Triangle is isosceles therefore, two shorter sides are equal. Let x be the shorter side than according to the triangle inequality theorem:

x + x > 12

2x > 12

x > 6

The smallest possible length of one of the two congruent sides is 6.1 cm rounded to the nearest tenth.

For more information, refer the link given below:

link

i dont know sorry

step-by-step explanation: