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..
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
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.
Hypotenuse = 12
ReplyDeleteLet 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
you have made a hypotenuse
ReplyDeletethe height to they hypo is 12
and not the hypo
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.
ReplyDeletePs-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..
Sorry..a*b/c=12
ReplyDeletehow is the damn triangle possible?(height:hypo=12)
ReplyDeleteThats for u to figure out
ReplyDeletesorry 150 .. the sides remain the same
ReplyDeleteAnswer is D) 300 .
ReplyDeleteThe sides are 15 , 20 , 25
my mistake, should have read the question a bit more carefully
ReplyDeleteLet the sides of triangle be a,b,c
ReplyDeleteand 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
one way is to get all values in terms of area A. now ,
ReplyDelete6h = 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.