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Bonus Question 26.07.09

with 13 comments


The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area?
(A) 75 (B) 144 (C) 150 (D) 300 (E) none of these

Written by Implex

July 26, 2009 at 11:20 am

13 Responses

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  1. Hypotenuse = 12
    Let the other two sides be a & b
    Now By Pythagora’s theorem we know

    a^2+b^2=12^2
    &
    a+b+12=60

    (a+b)^2 = 48^2
    – a^2 + b^2 + 2ab = 2304
    – 144+2ab = 2304
    – 2ab = 2160
    – Area = ab/2 = 540

    Ans e) None of the above

    ymafreak

    July 26, 2009 at 7:54 pm

    • you have made a hypotenuse

      the height to they hypo is 12
      and not the hypo

      Rahul

      July 26, 2009 at 8:05 pm

    • let a,b,c be the sides with c being the hypo.given a*b/c=60 . Given perimeter is 60.trying out the 3:4:5 combination,we get a=15,b=20,c=25.therefore area=150.

      Ps-I tried out the 3:4:5 combination because of the cat constraint of solving this within 1 minute.Great going Rahul..hope u convert IIMA this time..

      abhitsian

      July 27, 2009 at 5:16 am

  2. Sorry..a*b/c=12

    abhitsian

    July 27, 2009 at 5:24 am

  3. how is the damn triangle possible?(height:hypo=12)

    anonymous

    July 28, 2009 at 6:41 am

    • Thats for u to figure out

      Rahul

      July 28, 2009 at 6:59 am

  4. Answer is D) 300 .
    The sides are 15 , 20 , 25

    Hari

    July 28, 2009 at 9:32 am

  5. sorry 150 .. the sides remain the same

    Hari

    July 28, 2009 at 9:33 am

  6. my mistake, should have read the question a bit more carefully

    anonymous

    July 29, 2009 at 4:04 pm

  7. Let the sides of triangle be a,b,c
    and height to hypotenuse be h
    therefore we get h*c = a*b (c is the hypotenuse)
    this we got by equating area of the triangle

    h =12 (given)
    ab = 12c
    also
    a+b+c = 60 (given)
    a*a + b*b = c*c (pythogoras theorem)—-I

    a+b = 60 -c
    squaring and using I we get
    2ab = 3600 -120c
    but ab = 12c
    therefore
    c = 3600/144
    c = 25
    now the triplet is open so is area
    150 answer

    jatin

    August 28, 2009 at 9:19 am

    • what is this formula ab/c = h?
      And how is height to hypotenuse different from side of the triangle?

      Venkatadiri

      July 27, 2012 at 3:58 am

  8. one way is to get all values in terms of area A. now ,
    6h = A, h=sqrt(a^2+b^2) = A/6
    ab = 2A,
    given that h + a + b = 60
    =>A/6 + sqrt(a^2 +b^2+2ab) = 60
    substituting values you get a linear( as A^2/36 is eliminated on both sides) equation in A.solve easily to get A = 150.

    Pranshu

    November 10, 2009 at 3:04 pm

  9. 1.we have to find the pythagoras triplet which add up to 60
    2.general form of pythagoras trio is:(3n,4n,5n)
    3.when we put n=5 we get the trio as (15,20,25)
    4.base=25 ht=12;we can apply fromula for triangle area
    1/2*12*25=150

    vinit

    April 24, 2015 at 8:40 am


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