The height drawn to the base of the isosceles triangle is 20 cm, and to the lateral side is 24 cm. Find the perimeter of the triangle.

Given:
ABC – isosceles triangle,
AB, BC – lateral sides,
AB = BC = 24 centimeters,
ВН – height,
BH = 20 centimeters.
Find the perimeter of Ravs -?
Decision:
1) Consider a right-angled triangle ABН. Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AH ^ 2 + BH ^ 2 = AB ^ 2;
AH ^ 2 = AB ^ 2 – BH ^ 2;
AH ^ 2 = 24 ^ 2 – 20 ^ 2;
AH = 4√11 centimeters;
2) Consider an isosceles triangle ABC. In it AB = BC. The ВH height is also the median. Then AC = 2 * AH = 2 * 4√11 = 8√11;
3) Ravs = 24 + 24 + 8√11 = 56√11 centimeters.
Answer: 56√11 centimeters.