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syhna

find the radius of the largest circle that can be inscribed in a triangle with sides 5 cm, 7 cm, 10 cm respectively

  • one year ago
  • one year ago

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  1. matricked
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    let r be the radius of the largerst circle that can be drawn inside traingle then area of the triangle is given by the sum of the three triangles thus formed by joining the incentre with the respective vertices

    • one year ago
  2. matricked
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    thus r = area of triangle /(semi-perimeter of the triangle)

    • one year ago
  3. matricked
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    area of triangle= sqrt(11*1*6*4)=sqrt (264) =16.248 semi-perimetr= (5+7+10)=22/2=11 thus r =16.248/11 =1.477

    • one year ago
  4. syhna
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    i dont get it? i also solved it but in a different solution but i wasn't sure of my answer so i asked the question but our solutions and answers did not match so will you explain to me your solution ? pleeaase?

    • one year ago
  5. matricked
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    see first of all roughly draw the incircle touching all the sides of the triangle

    • one year ago
  6. matricked
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    now take any one side and see it forms a triangle with the incentre as one of the vertex and the side of the triangle as the base

    • one year ago
  7. syhna
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    |dw:1358145014344:dw| is the drawing supposed to be like this?

    • one year ago
  8. matricked
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    if i assume the lengths of the sides to be a,b,c (and say a=5,b=7,c=10) and r be the incenter of the triangle ,. then area of triangle is given by area =sqrt(s*s-a)*(s-b)*(s-c)) also when the triangle is subdivided into three tr

    • one year ago
  9. syhna
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    |dw:1358145137085:dw|

    • one year ago
  10. syhna
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    A = sqrt(11(11-5)(11-7)(11-10) right?

    • one year ago
  11. matricked
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    yup

    • one year ago
  12. matricked
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    also if r is the incentre then area=1/2 *r *5 + 1/2 *r *7 + 1/2 *r *10 =r *(5+7+10) /2 =r*22/2=11 *r hence 11r =sqrt(11(11-5)(11-7)(11-10) or r = (sqrt(11(11-5)(11-7)(11-10))/11

    • one year ago
  13. matricked
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    u can correct or check the calcualtion

    • one year ago
  14. syhna
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    1.47 cm?

    • one year ago
  15. syhna
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    thanks :)

    • one year ago
  16. matricked
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    welcome

    • one year ago
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