Multiple choice

The radius of a circle inscribed in a triangle length of whose sides are 3 units, 4 units and 5 units is

  1. 1 unit

  2. √2 units

  3. 2 units

  4. 3 units
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A Correct answer
Explanation

For a right-angled triangle (3, 4, 5), the inradius r = (a + b - c) / 2 = (3 + 4 - 5) / 2 = 2 / 2 = 1 unit.

AI explanation

The triangle with sides 3, 4, and 5 is a right-angled triangle because 3 squared plus 4 squared equals 5 squared. Using the formula for the inradius of a right triangle, r equals the sum of the legs minus the hypotenuse, all divided by 2. Substituting the values gives r equals (3 plus 4 minus 5) divided by 2, which simplifies to 1. The radius is 1 unit.

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