Ultimate Quant Marathon Blog For IIM CAT

Bonus Question 26.07.09

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11 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

   Reply
   • you have made a hypotenuse

     the height to they hypo is 12
     and not the hypo

     Rahul

     July 26, 2009 at 8:05 pm

     Reply
   • 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

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

   abhitsian

   July 27, 2009 at 5:24 am

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

   anonymous

   July 28, 2009 at 6:41 am

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   • Thats for u to figure out

     Rahul

     July 28, 2009 at 6:59 am

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

   Hari

   July 28, 2009 at 9:32 am

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5. sorry 150 .. the sides remain the same

   Hari

   July 28, 2009 at 9:33 am

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

   anonymous

   July 29, 2009 at 4:04 pm

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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

   Reply
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

   Reply