The side of an isosceles triangle is 25, and the height dropped on it is 24. Find the perimeter.

When holding the height in an isosceles triangle, we get two equal right-angled triangles, in which the height is the common leg, and 1/2 of the base is the second leg.

The lateral side of an isosceles triangle is the hypotenuse.

Since we know the hypotenuse and one of the legs, we determine the second leg using the Pythagorean theorem.

c ^ 2 = c ^ 2 – a ^ 2 = 25 ^ 2 – 24 ^ 2 = 625 – 576 = 49.

√49 = 7 cm (1/2 part from the base).

Find the base of the triangle.

7/1/2 = 7 * 2/1 = 14 cm.

Thus, the perimeter of the triangle will be:

P = 25 + 25 + 14 = 64 cm.

Answer: 64 cm.