Latest Elitmus Aptitude Question SOLUTION: Eiden park is a cricket field while jubilee park is football field in MastNagar. In MastNagar all cricket fields are circular and football fields are rectangle or square.Among the

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Eiden park is a cricket field while jubilee park is football field in MastNagar. In MastNagar all cricket fields are circular and football fields are rectangle or square.Among the boundary of all fields there are advertisement displays.In mastnagar length of advertisement displays must be same for all fields.Area of jubilee parks is 468m2.The farthest distance between any two points in jubilee park football field is 10sqrt10m.Find the approximate are of Eden park.
Options
A) 1936 m2 b)616 C)281 D) inadequate data

Asked In Elitmus Sumit Rawal (10 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Ravindra  (10 years ago)

@Sneha: Solution is here

farthest distance= Diagnol
if we assume jublie park as a square then result would be not match the side and the area, so this must be rectangular

for rectangular
area = l*b =468
and l^2+b^2=1000 because diagonal=10sqrt10
add 2lb both side
l^2+b^2+2lb=1000+2lb
(l+b)^2 = 1000+2*468
l+b=sqrt1936----------------------------------------eq1

as given already

2*pi*r=2(l+b)

pi*r=l+b-------------------------------eq2


put the value of l+b in eq1

pi*r=sqrt1936------------------------------ eq3

area of circle = pi*r^2

put the value of r here from eq3 616 will be answer

Is this solution Helpfull? Yes (38) | No (1)  

shweta sharma  (10 years ago)

ans B) 616

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Nani  (10 years ago)

Area=axb
468=axb
_________
(10sqrt10)^2=a^2+b^2
a^2+b^2=1000
(a+b)^2=a^2+b^2+2ab
on solving we get a+b=44, now perimeter=2(a+b)=> perimeter=88.
now area=pi*r^2
perimeter=2*(l+b)
A=pi*r^2
A=616m^2

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Harsha  (9 years ago)

l*b=468
l^2+b^2=1000
on solving both equations by hit and trial, we get,
l=26 and b=18
l+b=44
circumference of circle=circumference of rectangle
2*(22/7)*r=2(44)
on solving, r=14m
so, area of circle= (22/7)*14*14
area=616 square metres.

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C Ramya Udaya Chandrika  (8 years ago)

Let us consider the football field to be rectangular with dimensions L X B. Even if the

football field is square then we will get L = B.

Given Area of jubilee park = 468sqm.

Area of rect. park = LxB = 468 …… (i)

Farthest distance of field is diagonal ;

Therefore length of diagonal ; D = √L2+B2 = 10√10

or L2+B2 = 1000 …….. (ii)

Therefore; (L + B)2= L2+B2 + 2LB = 1000 + 2 x 468 = 1936

or , (L+B) = √1936 = 44

Therefore, Perimeter of rect. Field = 2 (L + B) = 2 x 44 = 88m

a/c to question; Perimeter of rectangular field = Circumference of Circular field

therefore, Circumference of Circular field = 2πR = 88m

Radius of circular field = 14m

Therefore Area of circular field = π142 = 616 sqm :-))

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Sneha Agarwal  (10 years ago)

@shweta how??

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C Ramya Udaya Chandrika  (8 years ago)

Can somebody make it more clear that the jublie park is a rectangle and why it is not a square?

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