Latest Elitmus Aptitude Question SOLUTION: A cricket is played in a Rhombus (all sides are equal) ground and the area of this field is 2400 m. The farthest distance is 80 m. and In this ground, Ice hockey is played in a cir

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(#M40019184) ELITMUS Numerical Ability question Keep an EYE

A cricket is played in a Rhombus (all sides are equal) ground and the area of this field is 2400 m. The farthest distance is 80 m. and In this ground, Ice hockey is played in a circular field. Find the area of Ice field (Circular field ).
a.1000/pie b.4000/pie c. 2500/pie d.i am not able to remember it right now

Asked In Elitmus (10 years ago)

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sushmita nigam  (10 years ago)

area=1/2*(product of diagonals)
longer diagonal is given as 80m
2400=1/2*80*d2
d2=60m(length of second diagonal)
since diagonals bisect at right angles
by pythagoras theorem we get,
s^2=40^2+30^2
s=50m(side of rhombus)
now drop a perpendicular from the meeting points of diagonals to the side of rhombus. the length of this perpendicular will be the radius of the required circle since diagonals are the angular bisectors of rhombus.
let the length of perpendicular be p
area of triangle formed=1/2(40*30)=600sqm
alternatively area is also 1/2(p*50)=600
p=24m
area of cicle will be=pie*r*r
= 576pie sqm

Is this solution Helpfull? Yes (57) | No (3)  

SAMBIT KUMAR GHOSH  (10 years ago)

Dear susmita,i solved this puzzle previously...u can see it in this page...but the in the last portion of the previous solution,i had mistaken it...so i just recorrect my solution..darling !!!

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sushmita nigam  (10 years ago)

dear sambit ghosh u have just copied my solution.............

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SAMBIT KUMAR GHOSH  (10 years ago)

i just do a silly mistake of my previous solution.after my previous solution we hav to consider the triangle formed by the diagonals.one of the triangle will beobp where o is the cutting point of the diagonals.op is the perpendicular distance from the cutting point of the diagonals i.e the radious of the circle.
1/2*ob*oc=1/2*30*40=600.now i.e equal to 1/2*50*op.
from here we get the value of op i.e equal to 24
then the radious of the circle is 24.
therefore the area of the circle is equal to pi*(24)^2=576*pi (ans).

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zen mano  (10 years ago)

radius of the circle is 24m.
area of the circle will be 1808 sq. meters.
multiply and divide by pie.
=(1808*pie)/pie

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Murugesan  (10 years ago)

80*80=6400(total Area of ground)
cricket=2400
ice hockey=total area-cricket
=6400-2000
=4000 (Sqr m)

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arpit farkya  (10 years ago)

area of rhombus=altitude*side
2400=80*side
side=30m.
so
area of circle=pi*r^2 //(r=radius of circle)
but by geometry we know that
r=30/2=15m.
s0 area of circle=pi*(15^2)=2250/pie that is correct

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SAMBIT KUMAR GHOSH  (10 years ago)

diagonal1=AC
AC=80
now area=1/2*AC*BD=2400 i.e 1/2*80*BD=2400 i.e BD=60
now we know that the diagonals of a rhombus bisect each other right angles
then,BC^2=BO^2+OC^2 i.e BC^2=30^2+40^2 i.e BC=50
now, radious of the circle will be 50/2=25
then the area of the circular field will be pi*(25)^2=625*pi(ans).

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