Answer:
Step-by-step explanation:
Let the shorter sides be x.
Given:
- Isosceles and acute triangle.
- Longer side is 8 cm.
To find:
- The length of the shorter sides, rounded to the nearest tenth.
Solution:
The angle at common vertex of congruent sides is less than 90°, since it is acute triangle.
It means the other congruent angles are greater than 45°, according to angle sum theorem.
The vertical bisector divides the triangle in half, with base 8/2 = 4 cm and hypotenuse x.
It gives us the inequality:
- 4/x < cos 45° ⇒
- x > 4 / cos 45° = 5.656
- x ≥ 5.7 cm
Correct choice is D
