## Bonus Question 26.07.09

**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**

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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

ymafreakJuly 26, 2009 at 7:54 pm

you have made a hypotenuse

the height to they hypo is 12

and not the hypo

RahulJuly 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..

abhitsianJuly 27, 2009 at 5:16 am

Sorry..a*b/c=12

abhitsianJuly 27, 2009 at 5:24 am

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

anonymousJuly 28, 2009 at 6:41 am

Thats for u to figure out

RahulJuly 28, 2009 at 6:59 am

Answer is D) 300 .

The sides are 15 , 20 , 25

HariJuly 28, 2009 at 9:32 am

sorry 150 .. the sides remain the same

HariJuly 28, 2009 at 9:33 am

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

anonymousJuly 29, 2009 at 4:04 pm

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

jatinAugust 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?

VenkatadiriJuly 27, 2012 at 3:58 am

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.

PranshuNovember 10, 2009 at 3:04 pm

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

vinitApril 24, 2015 at 8:40 am