# The perimeter of a triangle is 30 cm

Question:

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is

(a) $70 \mathrm{~cm}^{2}$

(b) $140 \mathrm{~cm}^{2}$

(c) $210 \mathrm{~cm}^{2}$

(d) $420 \mathrm{~cm}^{2}$

Solution:

We have to find the area of the given triangle.

Perimeter of triangle is 30 cm.

Let the radius of the circle be r.

We have,

Circumference of incircle $=88$

$2 \pi r=88$

$r=14$

Therefore,

$a r(\Delta \mathrm{ABC})=a r(\Delta \mathrm{OAB})+a r(\Delta \mathrm{OBC})+a r(\Delta \mathrm{OAC})$

$=\frac{1}{2}(r)(\mathrm{AB}+\mathrm{BC}+\mathrm{CA})$

$=\frac{1}{2}(14)(30) \mathrm{cm}^{2}$

$=210 \mathrm{~cm}^{2}$