In an isosceles triangle ABC AB = BC. Find AC if height BH = 8, AB = 10

Since, by condition, AB = BC, the triangle ABC is isosceles with the base AC.

ВН, by condition, is the height of triangle ABC, then triangles ABН and ВСН are rectangular.

According to the Pythagorean theorem, in a right-angled triangle, ABН, we determine the length of the leg AН.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 100 – 64 = 36.

AH = 6 cm.

The height BH of the triangle ABC is also its median, then AH = CH = 6 cm,

AC = AH + CH = 6 + 6 = 12 cm.

Answer: The length of the base of the speaker is 12 cm.