Latest TCS Aptitude Question SOLUTION: Given a square of length 2m. Its corners are cut such that to represent a regular octagon. Find the length of side of octagon.

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Given a square of length 2m. Its corners are cut such that to represent a regular octagon. Find the length of side of octagon.

Asked In TCS vishal kumar singh (11 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

kumar sundram  (11 years ago)

let us assume that every corner in every side cut by x m.
so, the length of side of octagon =2-(x+x)=2-2x=2(1-x)m.
from pythagoras' theorem, sqrt(x^2+x^2)=2-2x
or, x*sqrt(2)=2-2x
or, x(2+sqrt(2))=2
or, x=2/(2+sqrt(2))=2-sqrt(2)
thus, side of polygon=2(1-2+sqrt(2))=2*(0.4142)=0.8284m

Is this solution Helpfull? Yes (14) | No (3)  

M Sri Raviteja  (11 years ago)

Let a=length of side of polygon, r be inradius of octagon,n=8(number of sides of octagon)
then formula
a=2r*tan(pi/n) (pi=180degrees)
therefore lenght of side a=0.8284

Is this solution Helpfull? Yes (6) | No (1)  

rajesh ray  (11 years ago)

Let x is the side of the octagon and x + 2y is the side of the square.
In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2√
But x2√+x+x2√=2
⇒2√x+x=2
⇒x=22√ +1=22√ +1×2√ −12√ −1=2(2√ −1)

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

M Sri Raviteja  (11 years ago)

since it is given as square inradius r= (side of square)/2

Is this solution Helpfull? Yes | No (1)  

aastha rathore  (11 years ago)

use formula for side for side inscribed octagon.
we will have a/sqrt(2)+a+a/sqrt(2)=2
ans will be 0.823

Is this solution Helpfull? Yes | No (1)  

vivek baviskar  (11 years ago)

Let x is the side of the octagon and x + 2y is the side of the square.
In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2√
But x2√+x+x2√=2
⇒2√x+x=2
⇒x=22√ +1=22√ +1×2√ −12√ −1=2(2√ −1)

Is this solution Helpfull? Yes | No   

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