Latest ELITMUS Aptitude Question SOLUTION: There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle. OPTIONS: A.)24

• Placement Papers
• /
• ELITMUS
• /
• Category

ELITMUS Question Papers:

(#M40153653) ELITMUS Category question ELITMUS 13 SEP 2015 Keep an EYE

There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle.
OPTIONS:
A.)24cm B.)36*2^1/2cm C.)36cm D)54cm

Asked In ELITMUS Mithilesh kumar (8 years ago)

Unsolved Read Solution (7)

Is this Puzzle helpful?   (3)   (1) Submit Your Solution

Read Solution (7) :

Vikas Jha  (8 years ago)

For more illustration see the Wikipedia page of Right Angle Triangle...
Some Rules:-
1)The radius of the incircle of a right triangle with legs a and b and hypotenuse c is r=(a+b-c)/2
2)The radius of the circumcircle is half the length of the hypotenuse R=c/2
3)Thus the sum of the circumradius and the inradius is half the sum of the legs R+r=(a+b)/2

From 2nd Rule c=18cm
From 3rd Rule a+b= 2*(9+3) =24cm
Hence Perimeter a+b+c= 24+18= 42 cm Ans.
Now, I am not sure with the option you provided and there's confusion with option b).. but clearly a,c and d are not correct

Is this solution Helpfull? Yes (10) | No (1)  

Ajitesh rai  (8 years ago)

42 is the correct answer , It was mentioned in the option .

Is this solution Helpfull? Yes (4) | No   

Mayank Aditya  (8 years ago)

Answer is 42cm.
If you'll draw the fig.
u'll find hypotenuse of right angle triangle is 18.
hypotenuse can be divided in two parts: Let one is 'x' then other will be '18-x'(where it is touching the circle).
and when u'll apply the properties of tangent(perpendicular to radius), square and right angle triangle.
Let triangle have sides a, b and c(hypotenuse).
c=18.
a=18-x+3.
b=x+3.
perimeter= 18+18-x+3+x+3= 42.
so 42 is answer.

Is this solution Helpfull? Yes (3) | No   

Vidyakant soni   (8 years ago)

Logically for a right angle triangle with sides a, b, c b as hyp a+c>b... So option 24 and 36 is not possible... 54 means 18+18+18(as no side can be>18) which is also not possible.... So only possible answer... 36√2

Is this solution Helpfull? Yes (2) | No (3)  

kumar aashu  (8 years ago)

36*2^1/2 ans

Is this solution Helpfull? Yes | No (3)  

Arvind kumar yadav  (8 years ago)

b is the right ans

Is this solution Helpfull? Yes | No   

shailendra singh  (8 years ago)

its 54 cm....
1) Area of triangle= (a*b*c)/4R..... where R is circumradius
2)Area of triangle=S*r ...................where r is inradius and S is semiperimeter of the given triangle and it
is (a+b+c)/2...... where a,b,c are the sides of triangle
3) the area will be same because these are the area of same triangle
So equate these two........
we will get (a+b+c)=a*b/3
4) from Pythagoras theorem we will get a^2+b^2=18^2
and a*b= 9*18
5) from 3rd (a+b+c)=9*18/3..... which is equal to 54..:)

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.