Multiple Choice Question (MCQ)

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?

  1. ×

    12

  2. 24

  3. ×

    36

  4. ×

    12\sqrt{2}

Collected in the board: Triangle

Steven Zheng posted 3 weeks ago


Answer

  1. 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

Steven Zheng posted 3 weeks ago

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