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Meeta

· started a discussion

· 1 Months ago

Detailed answer (Question: 107654.0 )

Can anyone tell me how the numbers come 18, 9, 6 and 3.

Question:
The length of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. cm) of the triangle is:
Options:
A) 48
B) 144
C) 24
D) 72
Solution:
Ans: (d) Area of triangle = \(\cfrac{4}{3}\times\) Area of triangle formed by taking median as a side of triangle

  A= 9, B=12, C=15

  Side = \(\cfrac{A+B+C}{2}\) = \(\cfrac{9+12+15}{2} \)  = 18

   area of triangle =\(\frac{4}{3}\) \(\sqrt[]{S(S-a)(S-b)(S-c)}\)

 \(\cfrac{4}{3}\sqrt[]{18\times 9\times 6\times 3}\)

\(= \cfrac{4}{3}\times9 \times 3 \times 2=72\)

ABHII

· commented

· 1 Months ago

Dear student,
Please read the solution properly, S=18, 18 has been subtracted with each median A,B and C.Thus, 9,6 and 3 will come.
Best wishes.
Team TR

Kishan Kumar

· commented

· 1 Months ago

By heron formula √s(s-a)(s-b)(s-c)

Akash Yadav

· commented

· 1 Months ago

ya

Gopi Rayala

· commented

· 1 Months ago

root of s(s-a)(s-b)(s-c is formula of area where 2s=a+b+c

Saurav Kumar

· commented

· 1 Months ago

herons formula

MRIDULA SINGH

· commented

· 1 Months ago

using HERON'S FORMULA " [{s(s-a)(s-b)(s-c)}^(1/2)]" where s is semi perimeter and a,b,c are sides .

kanhaiya jha

· commented

· 1 Months ago

Let a triangle is ABC.
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
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