Latest TCS Aptitude Question SOLUTION: 9. How many different triangles with a perimeter of 15 cm can be constructed that have integral measurement of sides?

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9. How many different triangles with a perimeter of 15 cm can be constructed that have integral measurement of sides?

Asked In TCS ASD (10 years ago)

Unsolved Read Solution (12)

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Ann Mary Jolly  (10 years ago)

Ans : 7
1,7,7; 2,6,7; 3,6,6; 3,5,7; 4,5,6; 4,4,7; 5,5,5.
There are 7 possible triangles.

Is this solution Helpfull? Yes (19) | No (7)  

RAVI CHAND  (10 years ago)

let the perimeter be p.
no.of triangles if the odd numbered perimeter is given is p=2n-3.(where n is no.of triangles)
no.of triangles if the even numbered perimeter is given is p=2n.
given p=15cm.
hence 15=2n-3
n=9

Is this solution Helpfull? Yes (17) | No (3)  

Ashima Gupta  (10 years ago)

We have to find all choices of positive
integers x, y, and z such that

x + y + z = 15

x + y + z = 15
x + y > z
x + z > y
y + z > x

From
x + y + z = 15
x + y = 15 - z

and since x + y > z,
15 - z > z
15 > 2z
7.5 > z

From
x + y + z = 15
x + z = 15 - y

and since x + z > y,
15 - y > y
15 > 2y
7.5 > y

From
x + y + z = 15
y + z = 15 - x

and since y + z > x,
15 - x > x
15 > 2x
7.5 > x

So all the sides are 7 or less

And since to make sure they are non-congruent,

we'll require that x < y < z, so

x = 1 y = 7 z = 7
x = 2 y = 6 z = 7
x = 3 y = 5 z = 7
x = 3 y = 6 z = 6
x = 4 y = 4 z = 7
x = 4 y = 5 z = 6
x = 5 y = 5 z = 5

So there are 7.

Is this solution Helpfull? Yes (8) | No (3)  

prakash gupta  (10 years ago)

ans : 8
177,267,366,357,456,447,555,573

Is this solution Helpfull? Yes (4) | No (14)  

javed saifi  (10 years ago)

ans is 19
(1,1,13)(1,2,12)(1,3,11)(1,4,10)(1,5,9)(1,6,8)(1,7,7)(2,2,11)(2,3,10)(2,4,9)(2,5,8)(2,6,7)(3,3,9)(3,4,8)(3,5,7)(3,6,6)(4,4,7)(4,5,6)(5,5,5)

Is this solution Helpfull? Yes (3) | No (20)  

Sahil  (10 years ago)

14C2...AS Positive integral solution is given by (n-1)C(k-1)

Is this solution Helpfull? Yes (2) | No (4)  

subhrajit mitra  (10 years ago)

conditions are (1)a+b+c=15 & (2)summation of any two side > 3rd side
so the combinations are: (1,7,7)(2,6,7)(3,5,7)&(4,4,7)
therefore no of differnt triangles = 4

Is this solution Helpfull? Yes (2) | No (4)  

Shubham Yadav  (10 years ago)

Ans.7
771,627,555,564,573,636,645

Is this solution Helpfull? Yes (1) | No (1)  

subhrajit mitra  (10 years ago)

soorryy...ans will be 7

Is this solution Helpfull? Yes (1) | No (2)  

chandan kumar  (10 years ago)

ans 9.
(177),(267),(366),(357),(456),(447),(555),(573),(483).
all possible triangles

Is this solution Helpfull? Yes (1) | No (4)  

Guru Pranav  (10 years ago)

Sum of two sides should be greater than three sides. So, total number of triangles possible are 7
1,7,7; 2,6,7; 3,6,6; 3,5,7; 4,5,6; 4,4,7; 5,5,5.

Is this solution Helpfull? Yes (1) | No   

swati singh  (10 years ago)

perimeter of 15, the longest side must be 5, 6 or 7. If it is 5 then the middle side can be 5; if it is 6 then the middle side can be 5 or 6; if it is 7 then the middle side can be 4, 5, 6 or 7. Adding those up gives 1+2+4 = 7.

Is this solution Helpfull? Yes | No (3)  

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