Question

In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if AB = 21, AC = 28, and BC = 20.

Answer 1

Given : In triangle ABC, cevians AD and CF are bisectors. if AB = 21, AC = 28, and BC = 20.

To find : Find area ABC / area AFD

ConsTruction: Join seg FD

Solution: In the above figure, In

AD and CF are the cevians as well as the bisectors .........(1)

Now Taking ratios of AREAS OF 2 TRIANGLES

..................... (Both Have Common Heights).......(2)

Similarly

   .................... (3)

By Bisector Theorem, (Due to Statement 1)

      

Substituting the values,

By Componendo

........................... (B - D - C)

.........(Simplifying we get)....... (4)

Similarly

WORKING SIMILAR STEPS LIKE ABOVE (since A - F - B i.e. Componendo ), we get

  

....................... (5)

Multiplying 2 and 3 we get, and substituting the values of 4 and 5

Cancelling the common terms from Numerator and Denominator we get,  

Thats Your Answer !!!

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