If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :

Solution (By Examveda Team)

According to question,

Area of Δ(OBA + OAC + OBC) = area of ΔABC
$$\frac{1}{2}$$ × 4x × 3 + $$\frac{1}{2}$$ × 5x × 3 + $$\frac{1}{2}$$ × 6x × 3 = $$\frac{1}{2}$$ × (6x × AD)
$$\frac{1}{2}$$ × 3(4x + 5x + 6x) = $$\frac{1}{2}$$ × (6x × AD)
45x = 6x × AD
AD = $$\frac{{15}}{2}$$
AD = 7.5 cm