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Math Help - ..a very simple problem ..but different answers by different methods..

  1. #1
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    Question ..a very simple problem ..but different answers by different methods..

    ..a very simple problem ..but different answers by different methods..-tri.jpg
    (see attached fig).
    There is a triangle abc and an incircle to the triangle with radius 4cm.
    The area of the triangle is given to be 84 cm^2
    The base bc is divided by the radius into 6cm , 6cm
    ab = ac
    We need to find the value of these sides (ab or ac)
    ..
    Methods of solving :
    1)By using the pythagoras theorm, the answer comes to be appproximately 15 ( sqrrt(232) which is ~15
    2)while by using area (1/2bh) the answer comes to be exactly 15..
    what tis the reason for this difference?
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  2. #2
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    Quote Originally Posted by anshulbshah View Post
    2)while by using area (1/2bh) the answer comes to be exactly 15..
    what tis the reason for this difference?
    h = height
    6h = 84 ; h = 14
    sqrt(14^2 + 6^2) = sqrt(232)

    HOW did you get sqrt(225) ?
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  3. #3
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    Question

    Quote Originally Posted by Wilmer View Post
    h = height
    6h = 84 ; h = 14
    sqrt(14^2 + 6^2) = sqrt(232)

    HOW did you get sqrt(225) ?
    well i got it by a diff method..
    1)Join B and C to center (say o ) of the circle..
    2)Radius if perpendicular to BC ( tangent to a circle)
    therefore..
    ar(tri OBC) = 1/2 * 12 * 4 = 24cm^2
    area of entire fig =  84cm^2 thus area of remaining portion is 84 - 24 = 60
    now join point of contact of AC and AB to O ..these will be radius and perpendicular to AB and AC respectively..
    These will even be congruent ...as ab = ac & height / radius = 4cm
    thus area of these =  1/2 * base * 4 = 60 thus, base = 15cm
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  4. #4
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    the correctanswer to this problem is 15 because you must use the given in radius 4 to calculate the area .If you calculate that the altitude is 14 you would have a triangle with an in radius not equal to 4


    bjh
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  5. #5
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    Agree BJ. If area is 84 (as given) then height = 14: means radius = ~3.956

    anshulbshah, check your post for accuracy, please.
    If you want something similar to experiment with , use isosceles triangle 5-5-6:
    will have height 4 and inradius 3/2.
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