Hello,

Given that Radius of Incircle is √ 7 cm or can be written as 2.64 cm and Area of Triangle is 15 √ 7 cm

Area of Circle = π (radius) ² = π ( √ 7) ² = 21.98 cm ^2.

Perimeter of Circle  = 2πr = 2π (√ 7) = 16.62 cm

Now, Let side of the triangle be X cm

then Semi-perimeter S = 3X/2

Therefore, by putting the values in equation/formula -

Radius of Circle = Area of Triangle / Semi-perimeter

We get ,

√ 7 = (15√ 7) / (3X/2)

√ 7 = 30√7 / 3X

√ 7 x 3X =  30√ 7

3X = 30√ 7 / √ 7

X = 30√ 7 / 3√ 7

X = 10 cm.

Side of Triangle is 10 cm.

Since, all sides are same it is an equilateral triangle

Perimeter of equilateral triangle = 3 x Side

= 3 x 10 = 30 cm

Perimeter of Triangle is 30 cm.

Hope this was helpful.