Final answer:
The value of k is 2.
Step-by-step explanation:
The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Since all sides of an equilateral triangle are equal, we can divide the total perimeter by 3 to find the length of each side. In this case, the perimeter is 624 cm, so each side is 624 cm divided by 3, which is 208 cm.
The height of an equilateral triangle is a line segment perpendicular to the base and connecting the base to the opposite vertex. In an equilateral triangle, the height bisects the base and forms two right triangles. The height can be calculated by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the side of the triangle, which we already know is 208 cm. The other two sides are half the base (104 cm) and the height we are trying to find (k√3 cm). So we have the equation 104^2 + (k√3)^2 = 208^2. Solving for k, we find that k = 2.