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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z

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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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New post 06 Jun 2017, 10:25
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z and x, y, z represent the sides of each similar triangle. If the area of triangle ABC is twice the area of triangle abc, which of the following expresses X in terms of x?

A. \(\frac{x}{\sqrt{2}}\)

B. \(x\sqrt{2}\)

C. x/2

D. 2x

E. 4x

Attachment:
SimilarABC.png
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Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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New post 06 Jun 2017, 11:14
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Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
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Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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New post 12 Jan 2019, 15:33
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much! :)
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
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Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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New post 13 Jan 2019, 04:20
KHow,

Ratio of all the similar sides of XYZ to xyz is Sqrt 2.
X/x = Y/y = Z/z = Sqrt 2

Let me know if you got it.

Cheers!
Shantanu Sharma
INSEAD Class of December 2017
MBA and Beyond Consulting

KHow wrote:
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much! :)
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
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Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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New post 13 Jan 2019, 11:27
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B


Why is the area of Triangle ABC/Triangle abc = X^2/x^2? Where are the squares coming from?
GMAT Club Bot
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z   [#permalink] 13 Jan 2019, 11:27
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