The area of a triangle is 15 sq cm and the radius of its in circle is 3 cm. Its perimeter is equal to:

As per the given question,

Area of the triangle $$=15cm^2$$

Radius of the in circle=3cm

Let the side length of the AB, AC and BC are a, b and c.

From the above diagram, we can see that $$ar(\triangle ABC)=ar(\triangle AOB)+ar(\triangle AOC)+ar(\triangle BOC)$$

OD, OE and OF are the radius and the height of the inner triangle $$\triangle AOB, \triangle AOC$$ and $$\triangle BOC$$. so it will be equal.

Area of triangle = $$\dfrac{base\times height}{2}$$

So, $$15cm^2=\dfrac{a\times r}{2}+\dfrac{b\times r}{2}+\dfrac{c\times r}{2}$$

$$\Rightarrow 15cm^2\times 2=r(a+b+c)$$

$$\Rightarrow 3(a+b+c)=15cm^2\times 2$$

$$\Rightarrow (a+b+c)=\dfrac{15cm^2\times 2}{3}=10cm$$