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In the diagram to the below, the value of x is closest to which of the

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In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 08:18
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In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post Updated on: 11 Mar 2020, 17:45
Asad wrote:
In the diagram to the below, the value of \(x\) is closest to which of the following?

A) \(2+√2\)
B) \(2\)
C) \(√3\)
D) \(√2\)
E) \(1\)




Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = \(\sqrt{3}\)

Answer C
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Originally posted by sujoykrdatta on 11 Mar 2020, 11:39.
Last edited by sujoykrdatta on 11 Mar 2020, 17:45, edited 1 time in total.
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In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post Updated on: 11 Mar 2020, 18:36
sujoykrdatta wrote:
Asad wrote:
In the diagram to the below, the value of \(x\) is closest to which of the following?

A) \(2+√2\)
B) \(2\)
C) \(√3\)
D) \(√2\)
E) \(1\)




Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = 2

Answer B


\(√3.33\) = \(1.8\)
1.8 is closed to \(√3\). So the correct choice is C, actually.
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Originally posted by TheUltimateWinner on 11 Mar 2020, 12:16.
Last edited by TheUltimateWinner on 11 Mar 2020, 18:36, edited 1 time in total.
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Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 12:53
Asad wrote:
sujoykrdatta wrote:
Asad wrote:
In the diagram to the below, the value of \(x\) is closest to which of the following?

A) \(2+√2\)
B) \(2\)
C) \(√3\)
D) \(√2\)
E) \(1\)




Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = 2

Answer B


\(√3.33\) = \(1.43\)
1.43 is closed to \(√3\). So the correct choice is C, actually.



How is \(√3.33\) = \(1.43\)?

\(1.4^2 = 1.96\)
\(1.5^2 = 2.25\)
\(1.8^2 = 3.24\)
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Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 14:12
IMO ans is 1

Its an iso . triangle bcoz it has 2 equal sides.
One of the angle is 45 so the other one is also 45( same sides)

Its a 45 45 90 triangle.
The sides of 45 45 90 triangles are in ratio of 1 1 root 2.
Hypo is root 2 therefore x is 1

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In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 15:55
sujoykrdatta wrote:
Asad wrote:
In the diagram to the below, the value of \(x\) is closest to which of the following?

A) \(2+√2\)
B) \(2\)
C) \(√3\)
D) \(√2\)
E) \(1\)




Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = 2

Answer B

Hi sir, I think its closer to \(\sqrt{3}\).
\(\sqrt{3}\)=1.7. Your answer is 1.8. It is closer to 1.7 than 2.

Anyways my working is as follows -
\(2 = (\frac{x}{\sqrt{2}})^2 + (x - \frac{x}{\sqrt{2}})^2\)
\(or, 2 = 2x^2 -\frac{2x^2}{\sqrt{2}}\)
\(or, 1 = x^2 - \frac{x^2}{\sqrt{2}}\)
\(or, x^2 = \frac{\sqrt{2}}{(\sqrt{2}-1)}\)
\(or, x^2 = 1.4/0.4 = 3 (approx)\)
\(or, x = \sqrt{3}\)
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Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 17:47
AnirudhaS wrote:
sujoykrdatta wrote:
Asad wrote:
In the diagram to the below, the value of \(x\) is closest to which of the following?

A) \(2+√2\)
B) \(2\)
C) \(√3\)
D) \(√2\)
E) \(1\)




Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = 2

Answer B

Hi sir, I think its closer to \(\sqrt{3}\).
\(\sqrt{3}\)=1.7. Your answer is 1.8. It is closer to 1.7 than 2.

Anyways my working is as follows -
\(2 = (\frac{x}{\sqrt{2}})^2 + (x - \frac{x}{\sqrt{2}})^2\)
\(or, 2 = 2x^2 -\frac{2x^2}{\sqrt{2}}\)
\(or, 1 = x^2 - \frac{x^2}{\sqrt{2}}\)
\(or, x^2 = \frac{\sqrt{2}}{(\sqrt{2}-1)}\)
\(or, x^2 = 1.4/0.4 = 3 (approx)\)
\(or, x = \sqrt{3}\)



Yes obviously :roll:
I don't know what came of me :|
Must have not seen that option of root3 at all! :-D - corrected that - thanks

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Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
Admissions Consulting: http://www.oneclickprep.com/admissions-consulting/
IIT Kharagpur, TU Dresden Germany
Linked-in: https://www.linkedin.com/in/sujoy-kumar-datta/
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Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 11 Mar 2020, 18:44
sujoykrdatta wrote:
Asad wrote:
sujoykrdatta wrote:


Let us drawn AP perpendicular to BC as shown below:

Attachment:
111.JPG


In triangle APC: Angle ACP = Angle CAP = \(45^o\)

=> It is a 45-45-90 triangle

=> AP = PC = AC/\(\sqrt{2}\) = \(x/\sqrt{2}\)

=> BP = \(x - x/\sqrt{2}\)

In right triangle ABP: \(AB^2 = AP^2 + BP^2\)

=> \(2 = (x/\sqrt{2})^2 + (x - x/\sqrt{2})^2\)

=> \(2 = x^2/2 + x^2 + x^2/2 - 2x^2/\sqrt{2}\)

=> \(2 = x^2 * (2 - \sqrt{2})\)

=> \(x^2 = 2/(2 - \sqrt{2}) = ~ 2/0.6 = 3.33\) (approximately)

=> \(x = \sqrt{3.33} = 1.8\)

=> Closest value = 2

Answer B


\(√3.33\) = \(1.43\)
1.43 is closed to \(√3\). So the correct choice is C, actually.



How is \(√3.33\) = \(1.43\)?

\(1.4^2 = 1.96\)
\(1.5^2 = 2.25\)
\(1.8^2 = 3.24\)

My calculator gave me wrong info (value of root 3.33). I was convinced with that wrong value (1.43) because i already know that the correct choice is C.

Edited the first comment..

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Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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New post 29 Mar 2020, 06:15
I do not understand this question. When x and x are the same lengths, their respective angles have to have the same degree, right ? so i do not understand how anyonecan say this is a 45 - 45 - 90 triangle. If this was true root 2 has to be the longest side, so that the angles of 45 and 45 are respective to the two x.

In this case side root 2 faces the angle 45 so the angles for x are 135/2, so you can not use the pythagorean theorem to calculate the sides?
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Re: In the diagram to the below, the value of x is closest to which of the   [#permalink] 29 Mar 2020, 06:15

In the diagram to the below, the value of x is closest to which of the

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