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syhna

  • 2 years ago

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

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  1. matricked
    • 2 years ago
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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

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

  3. matricked
    • 2 years ago
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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

  4. syhna
    • 2 years ago
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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?

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

  6. matricked
    • 2 years ago
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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

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

  8. matricked
    • 2 years ago
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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

  9. syhna
    • 2 years ago
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    |dw:1358145137085:dw|

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

  11. matricked
    • 2 years ago
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    yup

  12. matricked
    • 2 years ago
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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

  13. matricked
    • 2 years ago
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    u can correct or check the calcualtion

  14. syhna
    • 2 years ago
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    1.47 cm?

  15. syhna
    • 2 years ago
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    thanks :)

  16. matricked
    • 2 years ago
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    welcome

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