The height of an equilateral triangle is 25 √3. Find the perimeter.

Since the triangle is equilateral, AB = BC = AC.

In an equilateral triangle, the height coincides with the median of the triangle, therefore, AH = CH.

Let AH = CH = X cm, then AB = BC = 2 * X.

Consider a right-angled triangle ABN, and by the Pythagorean theorem we find AB.

AB ^ 2 = BH ^ 2 + AH ^ 2.

(2 * X) ^ 2 = (25 * √3) ^ 2 + X ^ 2.

4 * X ^ 2 = 1875 + X ^ 2.

3 * X ^ 2 = 1875.

X ^ 2 = 1875/3 = 625.

X = 25 cm.

AB = BC = AC = 2 * X = 2 * 25 = 50 cm.

Then Ravs = 3 * 50 = 150 cm.

Answer: The perimeter of the triangle is 150 cm.