Question

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

• A. $10cm$
• B. $8cm$
• C. $7.5cm$
• D. $6cm$

Answer 1

The correct option is A $10cm$

Let the sides be 4x,5x,6x respectively.

As largest side is the base, therefore corresponding altitude (h) is given by

Inradius $r=\frac{Areaoftriangle}{Semi-perimeter}$

$\Rightarrow 3=\frac{\frac{1}{2}\times 6x\times h}{\frac{15x}{2}}$

$\Rightarrow h=\frac{3\times 15}{6}=7.5cm$