Latest Elitmus Aptitude Question SOLUTION: A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs, also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the appr

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(#M40152237) ELITMUS Numerical Ability question Geometry Keep an EYE

A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,
also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs

(a)6root(3) (a)12root(3) (a)9root(3) (a)18root(3)

Asked In Elitmus prem kishor (8 years ago)

Unsolved Read Solution (8)

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SHANUR RAHMAN  (8 years ago)

AS THE AREA OF SQUARE IS 36... THEN ONE SIDE WILL BE 6...AND THE PERIMETER OF SQUARE WOULD BE 24=PERIMETER OF PQRS......(1)

AND BY GIVEN CONDITIONS WE KNOW THAT PQRS IS A CASE OF ISOCLESS TRAPEZIUM..AS PQ IS PARALLEL TO RSAND PS=QR..

NOW BY (1)....
PQ+RS+QR+PS=24
3RS+QR+RS+QR=24
2RS+QR=12
NOW BY HIT AND TRIAL
PQ=9
QR=PS=6
SR=3
NOW WE CAN FIND THE HEIGHT OF TRAPEZIUM PQRS
WHICH WILL BE 3ROOT3....
AREA OF TRAPEZIUM= 1/2 *SUM OF PARALLEL SIDES *HEIGHT....
=1/2*(9+3)*3ROOT3
= 18ROOT3.

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Soumen Maity  (8 years ago)

Ans 18root(3)

Sol- Lets take, QR=PS= a m and RS=b m, So, PQ=3b m
now if are of a square is 36 sqm, then perimeter is 24

now perimeter of the inscribed quadrilateral is 4b+2a= 24
so, 2b+a=12
from this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)

Now, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}
Here s= 12
now by trial and error method we can get the solution

appprox area is 18root(3)

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Abhinav Anand  (8 years ago)

sorry in above solution it should be 4x+2y=24

as area of square is 36 so side of square is 6
so perimeter of squre =4*6=24
now
perimeter of quadriltrl=4x+2y=24 (acordng 2 ques)
and as we know sum of opposite sides of qudrilatal are equal
s0 4x=2y..
now solving both equation we get sides ofqudriltrl 9,6,3,6
now by appling formula of qudriltrl i.e sqrt(s-a)(s-b)(s-c)(s-d) we get the result as 18 root3
ans =18root3
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Abhinav Anand  (8 years ago)

as area of square is 36 so side of square is 6
so perimeter of squre =4*6=24
now
perimeter of quadriltrl=4x=2y=24 (acordng 2 ques)
and as we know sum of opposite sides of qudrilatal are equal
s0 4x=2y..
now solving both equation we get sides ofqudriltrl 9,6,3,6
now by appling formula of qudriltrl i.e sqrt(s-a)(s-b)(s-c)(s-d) we get the result as 18 root3
ans =18root3

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sitanshu  (8 years ago)

I didn't understand the following line submitted by you Abhinav Anand :
perimeter of quadriltrl=4x=2y=24 (acordng 2 ques)
Please Explain.

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tariq aziz  (8 years ago)

@Abhinav Anand-

but that property holds true when a quadrilateral is inscribed in a circle, but here its vice versa!!

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SANTU MAITY  (8 years ago)

option (d)18 root(3)

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Atharva Waze  (3 years ago)

18root(3)
use herons formula where s= 12

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