Suppose \triangle ABC is a triangle with area 24 and that there is a point P inside \triangle ABC which is distance 2 from each of the sides of \triangle ABC. What is the perimeter of \triangle ABC?

×
12

✓
24

×
36

×
12\sqrt{2}
Suppose \triangle ABC is a triangle with area 24 and that there is a point P inside \triangle ABC which is distance 2 from each of the sides of \triangle ABC. What is the perimeter of \triangle ABC?
12
24
36
12\sqrt{2}
Since it has the same distance from each of the sides of \triangle ABC , the point P is the origin of the inscribed circle of the triangle.
A = \dfrac{1}{2}(a+b+c)r
in which A is the area of the triangle and r is the radius of the inscribed circle.
The perimeter of the triangle is
a+b+c = 2A/r = 24