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FoolForMath

Fool's problem of the day, A not so easy geometry problem, A triangle is divided into four parts by straight lines from two of the corners. The area of three triangular parts are 8,5 and 10 sq units. What is the area of the remaining part? Good luck!

  • one year ago
  • one year ago

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  1. FoolForMath
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    |dw:1338105988238:dw|

    • one year ago
  2. FoolForMath
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    The diagram is not to scale.

    • one year ago
  3. ninhi5
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    does any of the line equal?

    • one year ago
  4. ninhi5
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    i'd take it as a no

    • one year ago
  5. shivamsinha
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    answer is 22

    • one year ago
  6. FoolForMath
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    Explain~

    • one year ago
  7. shivamsinha
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    1 sec

    • one year ago
  8. FoolForMath
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    http://www.pagalguy.com/forum/quantitative-questions-and-answers/71240-official-quant-thread-cat-2011-a-796.html doesn't have the solution right?

    • one year ago
  9. shivamsinha
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    oo thanks.... i am seeing this now!! wat u trying to prove ??

    • one year ago
  10. FoolForMath
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    I am interested to see your solution :)

    • one year ago
  11. shivamsinha
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    i m drwing it

    • one year ago
  12. FoolForMath
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    Take your time :)

    • one year ago
  13. shivamsinha
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    here it is i.ve assumed the base to be BC and the upper vertex to be A p is d pt. dropped frm vertex b at AC q is d pt. dropped frm vertex c at AB nd O is d pt. whr BP and CQ intersect each othr join PQ nw in tri. bpc areaBOC is twice of areaCOP so BO must b twice of PO and area of POQ cmes out to be 4(areaBOQ is 8) in tri.AQC(PQ is still joind) areaAQP/areaCPQ=AO/CO nd in tri.ABC areaABP/areaBPC=AO/CO THEREFORE(let areaAQP is X) areaAQP/areaCPQ=areaABP/areaBPC on solving areaAQP=18 so area of the remaining part in abc= 18+4=22

    • one year ago
  14. eliassaab
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    That is a short version of the above solution: Join the third vertex to the intersection of the two lines. Let x and y be the areas of the two triangles formed, with y near 8 and x near 5 \[ x = \frac 1 2 (y+8)\\ y= \frac 8 {10} (x+5) \] Solve, you get x=10, y= 12 and x+y =22

    • one year ago
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