Question

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

Options

• 70 cm²

• 140 cm²

•  210 cm²

• 420 cm²

Answer 1

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`

                               `2pi r=88`

                                   `  r=14`

Therefore,

`ar (ΔABC)=ar (ΔOAB)+ar (ΔOBC)+ar(ΔOAC)`

             ` = 1/2 (r)(AB+BC+CA)`     

            `= 1/2 (14)(30) cm^2`     

            `= 210 cm^2`