Latest Elitmus Aptitude Question SOLUTION: a quadrilateral PQRS circumscribes a circle with centre o,it is given that PQ is parallel to RS.Also length of PQ is thrice that of RS while length of QR and PS are equal.however Q

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(#M40010430) ELITMUS Numerical Ability question Keep an EYE

a quadrilateral PQRS circumscribes a circle with centre o,it is given that PQ is parallel to RS.Also length of PQ is thrice that of RS while length of QR and PS are equal.however QR and SP are not parallelto each other.the perimeter of the quadrilateral is equal to the perimeter of a square with area 36sq.m,what is the area of the quadrilateralPQRS in sqm(approx)??

Asked In Elitmus (11 years ago)

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Mayuresh Srivastava  (10 years ago)

18*sqrt(3) or 12r(if in terms of r where r-radius of circle)

Is this solution Helpfull? Yes (18) | No (4)  

ankur trivedi  (11 years ago)

in this question PQ||RS.
and let length of rs= x meter
then the length of PQ=3x meter.
now let the length of PS=y meter
then the length of RS will be y meter.
but QR and SP are not || .
and the perimeter of quadrilateral =perimeter of square with area 36 m^2.
so the side of square will be 6 m and perimeter will be 4*6 ie 24 meter.
so perimeter of quadrilateral will be =24 meter according to question.
and now we know that if a quadrilateral is circumscribed about a circle,then the sum of opposite sides are always equal.
so x+3x=y+y ie 4x=2y ie y=2x.
and the perimeter will be of quadrilateral =x+3x+y+y. =24
4x+2y=24.
now put the value of y=2x in this equation.
which gives x=3 and y=6.
so the side of quadrilateral will be 3,9,6,6.
and we know that area of quadrilateral =1/2*diagonal of quadrilateral*(sum of perpendicular on the diagonal ).
so in my think ans will be 30 m^2.

Is this solution Helpfull? Yes (14) | No (30)  

sonia nandi  (10 years ago)

in this question PQ||RS.
and let length of rs= x meter
then the length of PQ=3x meter.
now let the length of PS=y meter
then the length of RS will be y meter.
but QR and SP are not || .
and the perimeter of quadrilateral =perimeter of square with area 36 m^2.
so the side of square will be 6 m and perimeter will be 4*6 ie 24 meter.
so perimeter of quadrilateral will be =24 meter according to question.
and now we know that if a quadrilateral is circumscribed about a circle,then the sum of opposite sides are always equal.
so x+3x=y+y ie 4x=2y ie y=2x.
and the perimeter will be of quadrilateral =x+3x+y+y. =24
4x+2y=24.
now put the value of y=2x in this equation.
which gives x=3 and y=6.
so the side of quadrilateral will be 3,9,6,6.
and we know that area of circumscribed quadrilateral =[(s-a)(s-b)(s-c)(s-d)]^1/2
where s=(a+b+c+d)/2
so,s=12 and area of PQRS=18(3)^1/2 sq unit

Is this solution Helpfull? Yes (13) | No (2)  

Rahul kumar  (11 years ago)

Answer : 24*sqt(3)

Is this solution Helpfull? Yes (3) | No (8)  

sonia nandi  (10 years ago)

in this question PQ||RS.
and let length of rs= x meter
then the length of PQ=3x meter.
now let the length of PS=y meter
then the length of RS will be y meter.
but QR and SP are not || .
and the perimeter of quadrilateral =perimeter of square with area 36 m^2.
so the side of square will be 6 m and perimeter will be 4*6 ie 24 meter.
so perimeter of quadrilateral will be =24 meter according to question.
and now we know that if a quadrilateral is circumscribed about a circle,then the sum of opposite sides are always equal.
so x+3x=y+y ie 4x=2y ie y=2x.
and the perimeter will be of quadrilateral =x+3x+y+y. =24
4x+2y=24.
now put the value of y=2x in this equation.
which gives x=3 and y=6.
so the side of quadrilateral will be 3,9,6,6.
and we know that area of circumscribed quadrilateral =s[(s-a)(s-b)(s-c)(s-d)]^1/2
where s=(a+b+c+d)/2
so,s=12 and area of PQRS=98 sq unit

Is this solution Helpfull? Yes (3) | No (9)  

sarab  (10 years ago)

area will be 12*r ... where r is radius of the circle inscribed..

Is this solution Helpfull? Yes (2) | No (6)  

ravi prakash  (8 years ago)

using prop of isosceless trapezium (sum of opp sides are equal to other opp side)
ans=30

Is this solution Helpfull? Yes | No (1)  

Saumya  (8 years ago)

since the quadrilateral is inscribed in a circle.. sosum of opposite sides will be equal.
i.e 4RS=2QR
A/Q, perimeter of square equals to perimeter of qudrilateral
=>4RS+2QR=24
=>RS=3 AND QR=6
NOW, by drawing SM ll QR, and SD as height of triangle SMP we get euilateral triangle SMP from which SD=3root3
now, area of triangle is 9root3
area of parallelogram is 9root3
So, total area is 18root3

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