Question

12. В треугольнике ABC AH : HC = 2 : 3 и SAABс = 60 см².
Найдите площадь треугольника ВНС.​

Answer 1

S = (1/2) * a * h,

S_ABC / S_AHC = BC / HC = 3/2.

S_AHC = S_ABC * HC / BC = 60 * 2 / 3 = 40 см².

S_ABH / S_BCH = AH / HC = 2/3.

S_BCH = S_ABH * HC / AH = S_ABC * HC / (AH * 2) = 60 * 2 / (2 * 3) = 20 см².

h_BCH = 2 * S_BCH / BC = 2 * 20 / 3 = 40 / 3 см.

S_BNC = (1/2) * BC * h_BCH = (1/2) * 3 * (40/3) = 20 см².

Ответ: S_BNC = 20 см².