In the diagram, what is the value of x?

Question

geometry.png In the diagram, what is the value of x? A. 1+ sqrt(2) B. 1+ sqrt(3) C. 2sqrt(2) D. sqrt(2) + sqrt(3) E. 2sqrt(3) OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-diagram-what-is-the-value-of-x-129962.html

dreambeliever · Answer

i understood the OE provided but can someone help me find out what's wrong with my approach described in the attached?

jamifahad · Answer

How can you say A is the mid-point of DE? It is not the midpoint.

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dreambeliever · Answer

yeah, you are right. Angle bisector AB will not bisect the opposite side as DBE is a right triangle.

Thanks!

Spidy001 · Answer

let the triangle be ABC where AB = AC = x and BC = sqrt(2)

angle A of triangle ABC is 30 degrees. = > angle B = angle C = 75 (as its an isosceles triangle).

draw a perpendicular BD from B to AC . this forms two right angle triangles ABD and BCD.

ABD forms 30-60-90 triangle ,

where AB = x, AD = x * sqrt(3)/2 and BD = x/2 -------------equation 1

now consider BCD triangle,

where BD = x/2 ( from equation 1)
 BC = 2
 CD = x-(x*sqrt(3)/2)

using Pythagorean theorem we have
 BC^2 = CD^2+BD^2

Solving this will give x^2 = 2/(2-sqrt(3))

= 2(2+sqrt(3))
 
 = 4 + 2 sqrt(3)
 = (sqrt(3)^2) +1+ 2 * sqrt(3)
 
 = (1+sqrt(3)^2)

=> x = 1+sqrt(3)

Answer is B.

raghavakumar85 · Answer

Great question. I took nearly 6 minutes to answer this. Similar procedure explained by Spidy..

Is there a best way make an educated 'correct' guess for these questions and move on (when there is no sufficient time to solve)?

praveenvino · Answer

Please advise where i am wrong with this

Sin 30 = Opp side/Hyp side.

1/2 = sq(2)/x

x = sq(2)*2

KarishmaB · Answer

The trigonometric relations hold for right triangles.
When you say Sin 30 = 1/2, you are assuming that there is a RIGHT angle there. That's how you get the hypotenuse. This triangle has no right angle yet. How did you decide that hypotenuse is x? Hypotenuse is the side opposite the 90 degrees angle. There is no angle that is 90 degrees here.
BTW, good explanation by Spidy001. 
I am a little curious - what's the OE? Do they use trigonometry or something similar?

varunmaheshwari · Answer

I guess this cannot be solved without the use of Trigonometry!!

Spidy001, Thanks for the explanation!!

reatsaint · Answer

Excellent post , Spidy ..learnt a lot !!

Capricorn369 · Answer

Used my Trigonometry skills

The two isoscales base angles are 75 degrees each. Cos (45+30) = Cos (45) Cos (30) - Sin(45) Sin(30) Cos(75) = (\sqrt{3} - 1)/2 = 1/\sqrt{2}x Hence, x = \sqrt{3}+1 Answer B. Cheers!

arzad · Answer

B is the answer. it took me 4 minutes. Great Question and there is no need to use Cos and Sin.

samcot · Answer

i see,the best way to solve this is using cosine law or sin law.

2=2x^2-2x^2cos30
1=x^2(1-cos30)
x=1+sqrt3

or

x=sqrt2*sin75/sin30 =1+sqrt3

Bamsefar · Answer

How did you solve this without Cos and Sin?

MBAhereIcome · Answer

\sqrt{2}/sin30 = \frac{x}{sin75}

sin30 = 1/2 
 sin75 = (\sqrt{6}+\sqrt{2})/4

solve for x
 x = 1+\sqrt{3}

Bunuel · Answer

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-diagram-what-is-the-value-of-x-129962.html

In the diagram, what is the value of x?

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