The radius of the incircle of a triangle is √7cm. If the area of the triangle is 15√7cm. Find the perimeter.
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.