Latest Elitmus Aptitude Question SOLUTION: A right angle triangle inscribed in a circle of diameter 18cm and a circle of diameter 6cm inscribed in the triangle then what is the perimeter of triangle. A. 42 B. 36√2 C. 36 D

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(#M40037938) ELITMUS Category question Keep an EYE

A right angle triangle inscribed in a circle of diameter 18cm and a circle of diameter 6cm inscribed in the triangle then what is the perimeter of triangle.
A. 42
B. 36√2
C. 36
D. 24

Asked In Elitmus Gaurav Malhotra (9 years ago)

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RAKESH  (9 years ago)

let two sides of triangle be x,y
area of triangle = r*s where,r= inradius, s =semiperimeter

1/2 *xy = (x+y+18)/2 * 6/2
=> 2xy = 6(x+y) + 108

x^2 + y^2 = 18^2
=> (x+y)^2 - 2xy - 324 = 0
=> (x+y)^2 - 6(x+y) - 108 - 324 = 0
=> (x+y)^2 - 6(x+y) - 432 = 0
=> (x+y-24)(x+y+18)= 0
=> (x+y)= 24
perimeter = x+y+18 = 24 + 18 = 42

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Prateek Pandey  (9 years ago)

let the sides of the triangle be x,y,z.
Now,let the diamter of outer circle be the largest side of the right angled triangle i.e it's hypotenuse.x=18
we know dat (z+y-x)/2=inradius which is 3 in the given question
therefore,(y+z-18)/2=3,
above eqn gives y+z=24
the perimeter of the triangle is x+y+z=24+18=42

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amrita singh  (9 years ago)

ans is 42
since 18 is one of the side of the triangle. as we know sum of any two sides of the triangle should always be greater than the third one. so, if x,y(say) be the other two sides. den, x+y>18
->x+y+18>36
only option A. 42 matches d condition.

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