If the lengths 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 :
Let the sides of triangle be $$4x , 5x$$ and $$6x$$
Inradius(r) = 3 cm and semi perimeter(s) = $$\frac{4x+5x+6x}{2} = 7.5x$$
=> Area of triangle = $$r * s$$ = $$22.5x$$
Let altitude be $$h$$
Also area = $$\frac{1}{2} * 6x *h = 22.5x$$
=> $$h = \frac{22.5}{3} = 7.5$$cm
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