Latest TCS Aptitude Question SOLUTION: Explain clearly.......What is side of the largest possible regular octagon that can be cut out of a square of side 1 cm?

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Explain clearly.......What is side of the largest possible regular octagon that can be cut out of a square of side 1 cm?

Asked In TCS sashank (9 years ago)

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Read Solution (10) :

Akhilesh Kumar Ram  (9 years ago)

sorry,that was the wrong solution.The correct one is
length of side of octagon=sqrt(2)*[1/(2+sqrt(2))] [draw the geometrical figure]
=sqrt(2)*0.293
=0.41 cm

Is this solution Helpfull? Yes (8) | No   

PRADEEP KUMAR  (9 years ago)

let side of small triangle be x
then
x+sqrt(2)x+sqrt(2)x=1
on solving
x=0.3

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

Akhilesh Kumar Ram  (9 years ago)

length of side of octagon =sqrt(2)[(1/3)*side of Square]
=sqrt(2)*(1/3)
=1.414*(1/3)
=0.47 cm

Is this solution Helpfull? Yes (3) | No (2)  

supraja  (9 years ago)

let side of octagon be 'y'
one side of octagon occupies y length of square on respective side
part left on side of a square be (x+x) {i.e.,on both sides of its side equal part remains)
Therefore, 2x+y=1 cm
also there forms a right angled triangle with square two adjacent sides and a side of octagon
Hence by Pythagoras theorem,y=sqrt(x^2+x^2)=1.414*x
so, x=0.707*y
sub this in 2x+y=1,we get
2(0.707y)+y=1
Implies,y=0.414

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RISHABH  (9 years ago)

.44 cm
let side=x;
x+x/(sqrt(2)+x/(sqrt(2)=1
x=.44;

Is this solution Helpfull? Yes (2) | No (3)  

CHANDAN KUMAR  (9 years ago)

it can be best understand by drawing octagon in the square
let the side of octagon=x
renaining side of sq on each side of octagon=y,y
now y+x+y=1cm
x+2y=1, x=1-2y
now y^2+y^2=x^2
x^2=2y^2
(1-2y)^2=2y^2
y=1+/-0.707
taking value of y=1-0.707=0.293
so x=1-2y=1-2*0.293=0.414(ans)

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Atul Kumar  (9 years ago)

sqrt((1/3)^2 + (1/3)^2)=0.47

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

Ajish Raju  (9 years ago)

Draw a square and divide it into 9 equal blocks by drawing 2 horizontal and 2 vertical lines. Draw an octagon inside that square by joining points.
Now length of one side is simply 1/3=.33

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sashank  (9 years ago)

@rishabh can you say why x,x/sq2 please

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pooja chavan  (9 years ago)

draw the diagram
one side of squre in term of octagon =x+x+(1-2x)
angle made by octagon to square=45
by formula (x^2)*2=y
in triangle ,
cos45=x/y
x=0.707
y=.414cm

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