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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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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) $$1$$

Attachments figure.PNG [ 16.8 KiB | Viewed 711 times ]

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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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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 = $$\sqrt{3}$$

_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
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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.
SVP  V
Joined: 23 Feb 2015
Posts: 1944
In the diagram to the below, the value of x is closest to which of the  [#permalink]

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sujoykrdatta 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

$$√3.33$$ = $$1.8$$
1.8 is closed to $$√3$$. So the correct choice is C, actually.

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.
GMAT Tutor B
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GMAT 1: 740 Q51 V39
Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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sujoykrdatta 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

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

How is $$√3.33$$ = $$1.43$$?

$$1.4^2 = 1.96$$
$$1.5^2 = 2.25$$
$$1.8^2 = 3.24$$
_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
_________
Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS) | Let's converse!
Skype: sk_datta, Alt. Email: sujoy.datta@gmail.com
Manager  S
Joined: 11 May 2019
Posts: 108
Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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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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Joined: 30 Oct 2019
Posts: 486
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4
In the diagram to the below, the value of x is closest to which of the  [#permalink]

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sujoykrdatta 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

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 -
$$2 = (\frac{x}{\sqrt{2}})^2 + (x - \frac{x}{\sqrt{2}})^2$$
$$or, 2 = 2x^2 -\frac{2x^2}{\sqrt{2}}$$
$$or, 1 = x^2 - \frac{x^2}{\sqrt{2}}$$
$$or, x^2 = \frac{\sqrt{2}}{(\sqrt{2}-1)}$$
$$or, x^2 = 1.4/0.4 = 3 (approx)$$
$$or, x = \sqrt{3}$$
GMAT Tutor B
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
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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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AnirudhaS wrote:
sujoykrdatta 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

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 I don't know what came of me Must have not seen that option of root3 at all! - corrected that - thanks

Posted from my mobile device
_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
_________
Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS) | Let's converse!
Skype: sk_datta, Alt. Email: sujoy.datta@gmail.com
SVP  V
Joined: 23 Feb 2015
Posts: 1944
Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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sujoykrdatta 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

$$√3.33$$ = $$1.43$$
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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Intern  B
Joined: 12 Feb 2020
Posts: 4
Re: In the diagram to the below, the value of x is closest to which of the  [#permalink]

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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? 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  