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# Right triangles ABC and XYZ are similar. Each side of triangle ABC is

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Math Expert
Joined: 02 Sep 2009
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Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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07 Mar 2016, 07:55
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Difficulty:

25% (medium)

Question Stats:

70% (00:43) correct 30% (00:39) wrong based on 105 sessions

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Right triangles ABC and XYZ are similar. Each side of triangle ABC is x times the corresponding side of triangle XYZ. If x > 1, then the area of triangle XYZ is what fraction of the area of triangle ABC?

A. 1/x^2
B. 1/x
C. x
D. x^2
E. 2x^2
[Reveal] Spoiler: OA

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Kudos [?]: 139706 [0], given: 12794

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Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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08 Mar 2016, 02:35
Side of ABC = x * Side of XYZ

Area of ABC = $$x^2$$ * Area of XYZ

Area of XYZ = (1 / $$x^2$$) * Area of ABC

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Senior Manager
Joined: 20 Aug 2015
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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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09 Mar 2016, 00:27
1
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Expert's post
Bunuel wrote:
Right triangles ABC and XYZ are similar. Each side of triangle ABC is x times the corresponding side of triangle XYZ. If x > 1, then the area of triangle XYZ is what fraction of the area of triangle ABC?

A. 1/x^2
B. 1/x
C. x
D. x^2
E. 2x^2

Area of a triangle = 1/2 * Base * height

Since there are two lengths involved, hence the multiplication factor will be squared
Therefore if the lengths are in the ratio x, the are will be in the ratio $$x^2$$

Here each side of ABC is x times each side of XYZ
Therefore area of ABC = $$x^2$$ * area of XYZ

Hence Area of XYZ = 1/$$x^2$$ * Area of ABC
Option A

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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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09 Mar 2016, 11:53
1
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Area of Triangle = $$\frac{b*h}{2}$$

Desired Ratio = $$\frac{b*h}{2}$$*$$\frac{2}{(b*x*h*x)}$$ = $$\frac{2bh}{2bhxx}$$ = $$\frac{1}{x^2}$$

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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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10 Mar 2016, 08:05
Given: Each side is of triangle ABC= x* the corresponding side of triangle XYZ.
So,
Area of triangle ABC= 1/2.b.h.
Area of triangle XYZ= 1/2. (xb).(xh).

Therefore area of triangle XYZ to that of fraction of the area of triangle ABC = 1/x^2.

Guys this is my first post in this forum. Kindly let me know for any modifications.

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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is [#permalink]

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21 Dec 2017, 05:51
Hello from the GMAT Club BumpBot!

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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is   [#permalink] 21 Dec 2017, 05:51
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