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

Question

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

Uniteasy Admin · Accepted Answer

Since it has the same distance from each of the sides of $$	riangle ABC  $$, 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
$$a+b+c = 2A/r = 24 $$

Multiple Choice Question (MCQ)

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