ABC is an isosceles triangle (AB = BC). HH-height drawn to the base

ABC is an isosceles triangle (AB = BC). HH-height drawn to the base of the speaker. ВН refers to AS as 12:10. The perimeter of the triangle is 72. AB-?

We enter the proportionality coefficient x and we get that ВН = 12x, AC = 10x.
In the right-angled triangle ABН we find the hypotenuse AB (by the Pythagorean theorem):
AB = √ (BH² + AH²) = √ (144x² + 25x²) = √169x² = 13x.
The perimeter of the triangle is known by the condition, we draw up the equation:
13x + 13x + 10x = 72
36x = 72
x = 2.
AB = 13x = 13 * 2 = 26.
Answer: side AB is 26.