Latest Elitmus Aptitude Question SOLUTION: There is a square with side ‘a’ and one octagon is inscribed in it. What will be perimeter of octagon.

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There is a square with side ‘a’ and one octagon is inscribed in it. What will be perimeter of octagon.

Asked In Elitmus Sniper (7 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Aseem  (7 years ago)

let side of the octagon = f
as octagon is inscribed in the square
therefore
each side of square share 1 side of octagon and the remaining side left = a-f
since the corner of two side of square makes a right angled Isosceles triangle
therefore
[(a-f)/2]^2+[(a-f)/2]^2=f
f=(a-f)/root2
f=a/(root2+1)

perimeter of octagon is 8a/(root2+1)

Is this solution Helpfull? Yes (14) | No   

ROHIT YADAV  (7 years ago)

Well if it's a regular octagon then it actually trisects each side of the square in which 1/3 of the lenght of the side of the square is the length of one side of the octagon. If any one has a doubt he can draw the figure and see it
Going this way lenght of a side of a octagon is a/3 and thus perimeter would be 8a/3.

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

sandip kumar gupta  (7 years ago)

no. the ans will be 4a/3(1+root2)

Is this solution Helpfull? Yes (4) | No (2)  

sunil jain  (7 years ago)

8a/(sqrt(2)+1)

Is this solution Helpfull? Yes (2) | No   

Anamika Anand  (7 years ago)

The octagone trisects the square ,so side of octagone will be a/3.Now like perimeter of square is 4a ,the perimeter of otagone is 8a=8Xa/3=8a/3

Is this solution Helpfull? Yes (1) | No (7)  

shreesh  (7 years ago)

(root2-1)8a=3.31a

Is this solution Helpfull? Yes (1) | No (3)  

BHARAT KUMAR  (7 years ago)

Ans : 8a/3

Is this solution Helpfull? Yes | No (4)  

paras  (7 years ago)

perimter = 4 x a

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Devendra Nagar  (7 years ago)

Ans : 8a/3

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sunil kumar patra  (7 years ago)

4*(a/3)+4*root[(a/3)^2+(a/3)^2] = a/3(4+0.717) =4.71(a/3) ans

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Naveen babu  (7 years ago)

you cannot fix an octagon as you are imagining mr. Rohit

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pratik  (7 years ago)

8a/(1+2(root 2))

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