Final answer:
Only option (a) with x = 60° and a side length of 8 units forms an equilateral triangle, where all sides are equal in length and each angle measures 60 degrees.
Step-by-step explanation:
To determine which value of x makes the triangle equilateral and the length of each side, we need to recognize that an equilateral triangle has three equal sides and three angles, each measuring 60 degrees. With this in mind:
- a) x = 60°, Side length = 8 units: This triangle is already equilateral as the angle x is 60° and the sides are equal.
- b) x = 120°, Side length = 4 units: This cannot form an equilateral triangle as each angle in an equilateral triangle must be 60°.
- c) x = 90°, Side length = 6 units: This also cannot form an equilateral triangle since the angle indicates a right triangle.
- d) x = 45°, Side length = 10 units: This cannot form an equilateral triangle as the angles are less than 60°.
Out of the four options given, only the first option (a) is correct for forming an equilateral triangle; therefore, side length for each side in option (a) is 8 units.