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

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Math Expert
Joined: 02 Sep 2009
Posts: 50670
In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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06 Jun 2017, 09:25
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:13) correct 46% (01:37) wrong based on 70 sessions

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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 [ 10.2 KiB | Viewed 1927 times ]

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Posts: 331
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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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$$\sqrt{2}$$

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

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02 Nov 2018, 05:29
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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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