Multiple choice

What is the circumference of circle inscribed in a triangle having length of sides 35 cm, 44 cm and 75 cm? उस वृत्त की परिधि क्या है, जो 35 सेमी., 44 सेमी. और 75 सेमी. त्रिभुज में खींचा जाता है?

  1. 8 π cm./सेमी.

  2. 12 π cm./सेमी.

  3. 16 π cm./सेमी.

  4. 7.4 π cm./सेमी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For sides 35, 44, 75: s = (35+44+75)/2 = 77. Area = sqrt(77*42*33*2) = sqrt(212052) ≈ 460.5 cm². Inradius r = Area/s = 460.5/77 ≈ 5.98. Circumference = 2πr = 2π*4 = 8π. Wait, let me recalculate: sqrt(77*42*33*2) = sqrt(212052) ≈ 460.5. But notice: 35+44 = 79, which is > 75, so triangle is valid. Actually, r = A/s. But let's use formula: r = (a+b-c)/2 for any triangle? No, that's for right triangles. For any triangle, r = A/s. Let me recalculate: 77*42*33*2 = 212052. sqrt(212052) = 460.5. r = 460.5/77 = 5.98. Circumference = 2π*5.98 ≈ 37.6 = 12π (since 12π ≈ 37.7). Option B (12π) is correct.

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