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12 votes
12 votes
I need help finding out the answer

I need help finding out the answer-example-1
User Bhdrk
by
3.0k points

1 Answer

20 votes
20 votes

Answer:

  • D) 5.7 cm

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

User Shaunice
by
3.2k points