Latest Elitmus Aptitude Question SOLUTION: a circle whose diameter is 18cm, a right angled triangle is inserted in that circle, and a small circle whose diameter is 6cm inscribed in right angled triangle. find the perimete

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(#M40037951) ELITMUS Numerical Ability question area and volume Keep an EYE

a circle whose diameter is 18cm,
a right angled triangle is inserted in that circle,
and a small circle whose diameter is 6cm inscribed in right angled triangle.
find the perimeter of triangle

Asked In Elitmus Thireesha (9 years ago)

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RAKESH  (9 years ago)

triangle is right angled
so, diameter of circle is the hypotensue of triangle.

let other two sides of triangle are 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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