Multiple choice

The hypotenuse of a right angled triangle is $10\space cm$ and the radius of its inscribed circle is $1\space cm$. Therefore, perimeter of the triangle is

  1. $22\space cm$
  2. $24\space cm$
  3. $26\space cm$
  4. $30\space cm$
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A Correct answer
Explanation

For a right triangle, r = (a+b-c)/2, where c is the hypotenuse. 1 = (a+b-10)/2, so a+b = 12. Perimeter = a+b+c = 12+10 = 22.

AI explanation

Using the formula for the inradius of a right triangle, r equals (a + b - c) divided by 2, where c is the hypotenuse. Substituting the given values gives 1 = (a + b - 10) / 2, so a + b = 12. The perimeter is a + b + c, which is 12 + 10 = 22 cm.

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