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Thursday, 2 May 2013

Solution of (The lengths of three median. Of a triangle are 9cm 12 cm and 15cm.the area of triangle is)

The lengths of three median. Of a triangle are 9cm 12 cm and 15cm.the area of triangle is:


In this triangle medians AD =12, BE =9 and CF=15.
Because the median cut each other on centroid G in the ratio of 2:1 so the segments AG= 8, GD=4, BG=6, GE=3, CG=10 AND GF= 5

Now we take Triangle ABG, in this Triangle we are seeing that one side AG=8 and other side BG= 6 so the third side AB should be 10 and the triangle ABG is a right angled triangle making an angle 90 degree at the point G.

Now take a bigger triangle ABE. In this triangle we know that AG is perpendicular to BE and so the area of the Triangle ABE should be

1/2 AG*BE= 1/2 * 8*9 = 36

Now we know that any median of triangle bisects the triangle into two triangle of equal areas so the median BE bisects the Triangle ABC into two triangles, ABE and BED, of Equal area so 

area of ABE = area of BED = 36 so the area of triangle ABC= area of ABE+ area of BED = 36+36= 72


14 comments:

  1. What is triangle BED ??Cant infer from the above figure

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  2. Thanks for the explanation. It really helped.

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  3. This comment has been removed by the author.

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  4. How AB=10 cm and why ABG is a right angled triangle making an angle 90 degree at the point G ? Please explain.

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    Replies
    1. bcoz it follow pythagorous theorem

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    2. If the angle between the sides 6 and 8 be right angle then we can infer the third side to be 10 and vice-versa. The angle between the sides 6 and 8 need not necessary be right angle always.
      Sides with 6,8,11 also form a triangle but its not a right angled triangle.

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  5. Area= 4/3*square root of[s(s-a)(s-b)(s-c)]
    s=[a+b+c]/2
    s=[9+12+15]/2=18
    area= 4/3*square root of [18*(18-9)*(18-12)*(18-15)]
    Area=4/3*square root of [18*9*6*3]
    Area=4/3*square root of [9*2*9*3*2*3]
    Area=4/3*[9*2*3]
    Area=4*9*2
    Area=72

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    Replies
    1. I like it @Deendayal Poonia.Well done and thanks.

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    2. please drive that formula of area

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  6. This comment has been removed by the author.

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  7. If the angle between the sides 6 and 8 be right angle then we can infer the third side to be 10 and vice-versa. The angle between the sides 6 and 8 need not necessary be right angle always.
    Sides with 6,8,11 also form a triangle but its not a right angled triangle.

    ReplyDelete
  8. The formula is 2/3 × M1 ×M2 where M1 and M2 is the side which forms right angle

    ReplyDelete