The height of an isosceles triangle divides it into two equal right-angled triangles. In this way:
AB = BC;
AH = НС, and they have a common side ВН.
The height of an isosceles triangle is also the bisector of the angle opposite the base and divides it in half:
∠AВН = ∠НВС = ∠ABС / 2;
∠АВН = ∠НВС = 120º / 2 = 60º.
Consider the triangle ΔАВН. Using the cosine theorem, we find the length of the side AB:
cos B = HВ / AB;
AB = BH / cos B;
cos 60º = 1/2 = 0.5;
AB = 19.5 / 0.5 = 39 cm.
AB + BC = 39 + 39 = 78 cm.
Answer: the sum of the sides of an isosceles triangle is 78 cm.
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