Multiple choice

Perimeter of a triangle is $24\ cm$. Largest possible circle inscribed in it of radius $2\ cm$. Area of the triangle$=..$

  1. $24\ cm^{2}$
  2. $30\ cm^{2}$
  3. $36\ cm^{2}$
  4. $42\ cm^{2}$
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A Correct answer
Explanation

The area of a triangle is given by A = rs, where r is the inradius and s is the semi-perimeter. Here, s = 24 / 2 = 12 cm and r = 2 cm. Area = 2 * 12 = 24 cm^2.

AI explanation

Using the area formula involving the inradius, the area of the triangle equals the product of its semi-perimeter and its inradius. The semi-perimeter is half of 24 cm, which is 12 cm. Multiplying this by the given inradius of 2 cm gives an area of 24 square cm.

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