Latest Capgemini Aptitude Question SOLUTION: 2. A triangle has sides of lengths 10, 24 and n, where n is a positive n is a positive integer. The number of values of n for which this triangle has three acute angles is A. 1 B.

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2. A triangle has sides of lengths 10, 24 and n, where n is a positive n is a positive integer. The number of values of n for which this triangle has three acute angles is
A. 1
B. 2
C. 3
D. 4

Asked In Capgemini Akansha Sharma (8 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

venkatesh  (8 years ago)

triangle with acute angle:a^2+b^2>c^2
i)let a=10,b=n,c=24
so 10^2+n^2>24^2
n^2>(24^2-10^2)
n^2>576-100
n^2>476

ii)let a=10,b=24,c=n
10^2+24^2>n^2
100+576>n^2
676>n^2

so from i and ii
476>n^2>676 hence root476>n>root676
ans=22,23,24,25
sol:4

Is this solution Helpfull? Yes (17) | No   

Pranav Korpal  (8 years ago)

In an acute angled triangle; the sum of the squares of any two sides of a triangle have to be greater than the third side
i.e. 10^2+24^2>x^2 ; x^2+10^2>24^2 ;and x^2+>24^2>10^2 computing the minimum and maximum “x”, we get the range as 26>x>√476. the values of “x” which satisfy the above conditions are 22,23,24 and 25. Hence 4

Is this solution Helpfull? Yes (16) | No (4)  

ramya  (8 years ago)

a^2+b^2>c^2
10^2+24^2>c^2
c^224^2
b^2>476
so 476

Is this solution Helpfull? Yes (4) | No (11)  

Yella Suchitra  (8 years ago)

I think ans:3
n should be 22 or 23 or 25 to satisfy condition
a^2+b^2>c^2

Is this solution Helpfull? Yes (3) | No (5)  

ramya  (8 years ago)

a^2+b^2>c^2=>=>10^2+24^2>c^2
c^224^2=>=>b^2>476
so 476>>>so value is 4

Is this solution Helpfull? Yes (2) | No (7)  

sambhav jain  (7 years ago)

triangle with acute angle:a^2+b^2>c^2
i)let a=10,b=n,c=24
so 10^2+n^2>24^2
n^2>(24^2-10^2)
n^2>576-100
n^2>476

ii)let a=10,b=24,c=n
10^2+24^2>n^2
100+576>n^2
676>n^2

so from i and ii
476>n^2>676 hence sqrt(476)>n>sqrt(676)
ans=22,23,24,25
sol:4

Is this solution Helpfull? Yes (1) | No   

Swati Kumari  (8 years ago)

plzzz explain this properly

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