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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, 09:25
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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

Spoiler: ::
Attachment:
SimilarABC.png
SimilarABC.png [ 10.2 KiB | Viewed 1927 times ]
Spoiler: OA

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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, 10:14
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2
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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Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z &nbs [#permalink] 02 Nov 2018, 05:29
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