Latest Elitmus Aptitude Question SOLUTION: Q. The angles of 2 sides of quadrilateral B and D are 90 degree each. BP and DQ are perpendicular to diagonal AC and it trisects the AC(AP=PQ=QC). Side AB is 4cm then find perimete

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(#M40031283) ELITMUS Numerical Ability question Geometry Keep an EYE

Q. The angles of 2 sides of quadrilateral B and D are 90 degree each. BP and DQ are perpendicular to diagonal AC and it trisects the AC(AP=PQ=QC). Side AB is 4cm then find perimeter of quadrilateral.

Asked In Elitmus Himanshu Tyagi (11 years ago)

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RAKESH  (11 years ago)

B,D are 90 so its a rectangle
let AD=X then AC^2=(16+X^2) AP=AC/3
SO AP^2=AC^2/9=(16+X^2)/9
BP^2=AB^2-AP^2=16-{(16+X^2)/9}
equate area of triangle ABC
(1/2)*AC*BP = (1/2)*AB*BC
or AC^2*BP^2 = AB^2*BC^2
or (16+x^2)*[16-{(16+X^2)/9}]=16*x^2
after solving
x^4+32x^2-32*64=0
x^2= 32 or -64
x^2=32
so x=4*(sqrt 2)
perimeter of quadrilateral=2(x+4)
=2[4*(sqrt 2)+4]
=8(1+sqrt(2))

Is this solution Helpfull? Yes (16) | No (8)  

soma singha  (10 years ago)

https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-frc3/1476375_268402199980030_2069894024_n.jpg THIS IS THE IMAGE OF DIAGRAM ..

Is this solution Helpfull? Yes (8) | No (2)  

sivasankar  (11 years ago)

Rakesh could you please provide the diagram....please

Is this solution Helpfull? Yes (4) | No   

Atul  (10 years ago)

______________ _
A| / |D
| p / |
| / Q/ |
B|/___________ __|C

BP_|_AC
DQ_|_AC
AB_|_BC
DC_|_AD
so right angle traingles are ABC,DAC,ABP,DQC,BPC,ADQ...but we just need 3 of them
take ABC, ABP & BPC

AB=DC=4;
Let AD=BC=x;
Let AP=a;
so AC=3a;

from |_ ABC
x^2-16=9a^2; ---------(1)


from |_ ABP
BP^2=16-a^2 ---------(2)


from |_ BPC

16-a^2=x^2-4a^2 (use 2)
3a^2=x^2-16 ---------(3)

from (1) & (3)
x^2-16=3x^2-48
32=2x^2

x=4(2)^1/2

so perimeter=8+8(2)^1/2

Is this solution Helpfull? Yes (2) | No   

nandish  (11 years ago)

first,it may or may not be rectangle.
second,let us consider x to be 3 equally divided line segments.
so perimeter would be equal to 4*square root of (9x^2-y^2).

Is this solution Helpfull? Yes (1) | No (4)  

M.Lakshmi Durga  (11 years ago)

9 1's are there.dont confuse here
first multiply the numbers where ever multiplication symbol is present then go for repective binary format.then count number of 1's.u ll get it.

Is this solution Helpfull? Yes | No (1)  

Nancy neha  (11 years ago)

nt gettng d soln..could sm1 explain please..

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SHISHR KUMAR PANDEY  (11 years ago)

18 be the perimeter

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