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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 67% (01:16) correct 33% (01:17) wrong based on 160 sessions

### HideShow timer Statistics 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

_________________
Retired Moderator D
Joined: 13 Apr 2015
Posts: 1677
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1 GPA: 4
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Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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Side of ABC = x * Side of XYZ

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

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

Senior Manager  Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44 Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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1
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
Current Student B
Joined: 09 Feb 2014
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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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1
Area of Triangle = $$\frac{b*h}{2}$$

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

Intern  Joined: 25 Feb 2016
Posts: 3
Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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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. Non-Human User Joined: 09 Sep 2013
Posts: 11666
Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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_________________ Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is   [#permalink] 21 Dec 2017, 06:51
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# Right triangles ABC and XYZ are similar. Each side of triangle ABC is  