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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
Posted in Algebra, CAT 2009, Geometry, Mock Cat, Mock Quant, Online CAT, Problem of the week, Problems
Tagged with cat, CAT 2009, Geometry, IIM, Online CAT, Problem of the week
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Hypotenuse = 12
Let the other two sides be a & b
Now By Pythagora’s theorem we know
(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
July 26, 2009 at 7:54 pm
you have made a hypotenuse
the height to they hypo is 12
and not the hypo
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..
July 27, 2009 at 5:16 am
July 27, 2009 at 5:24 am
how is the damn triangle possible?(height:hypo=12)
July 28, 2009 at 6:41 am
Thats for u to figure out
July 28, 2009 at 6:59 am
Answer is D) 300 .
The sides are 15 , 20 , 25
July 28, 2009 at 9:32 am
sorry 150 .. the sides remain the same
July 28, 2009 at 9:33 am
my mistake, should have read the question a bit more carefully
July 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
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
c = 3600/144
c = 25
now the triplet is open so is area
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?
July 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.
November 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
April 24, 2015 at 8:40 am
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