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# A square, whose side is 2 meters, has its corners cut away

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NUS School Moderator
Joined: 18 Jul 2018
Posts: 1028
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
A square, whose side is 2 meters, has its corners cut away  [#permalink]

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12 Oct 2018, 09:14
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Difficulty:

55% (hard)

Question Stats:

50% (01:37) correct 50% (01:46) wrong based on 29 sessions

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A square, whose side is 2 meters, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon in meters is.

a) $$\frac{\sqrt{2}}{\sqrt{2}+1}$$
b) $$\frac{2}{\sqrt{2}+1}$$
c) $$\frac{\sqrt{2}}{\sqrt{2}-1}$$
d) $$\frac{2}{\sqrt{2}-1}$$
e) None of these

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A square, whose side is 2 meters, has its corners cut away  [#permalink]

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12 Oct 2018, 11:18
1
Afc0892 wrote:
A square, whose side is 2 meters, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon in meters is.

a) $$\frac{\sqrt{2}}{\sqrt{2}+1}$$
b) $$\frac{2}{\sqrt{2}+1}$$
c) $$\frac{\sqrt{2}}{\sqrt{2}-1}$$
d) $$\frac{2}{\sqrt{2}-1}$$
e) None of these

In the below square ABCD, we need to find the value of EF or GE (since both are equal)

In triangle AGE, AG=AE=x. Since it's an isosceles right angled triangle, GE=$$\sqrt{2}x$$ .(Sides are in the ratio 1:1:$$\sqrt{2}$$ )

EF= 2 - 2x (Since the side of square is 2)

Since EF=GE (Given Octagon with equal sides)

2-2x=$$\sqrt{2}x$$

On simplifying the above equation, we get x=$$\frac{\sqrt{2}}{\sqrt{2}+1}$$

We need to find the value of $$\sqrt{2}x$$, on simplification we get $$\frac{2}{\sqrt{2}+1}$$

Hence B.

Cheers!
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A square, whose side is 2 meters, has its corners cut away   [#permalink] 12 Oct 2018, 11:18
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