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NDA 2022 Maths · Mathematics · Properties of Triangles · medium

The inradius of a triangle with sides 13,14,15 is

Single correct option

The inradius of a triangle with sides 13,14,1513,14,15 is
  1. A. 33
  2. B. 44
  3. C. 66
  4. D. 214\dfrac{21}{4}
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Answer: (B) 44

The semi-perimeter is s=21s=21 and Heron's formula gives area 21⋅8⋅7⋅6=84\sqrt{21\cdot8\cdot7\cdot6}=84. Then r=Δs=8421=4r=\frac{\Delta}{s}=\frac{84}{21}=4. Dividing by the perimeter gives 22 instead.
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