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

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

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New post 07 Mar 2016, 07:55
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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

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

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New post 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

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

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New post 09 Mar 2016, 00:27
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
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Re: Right triangles ABC and XYZ are similar. Each side of triangle ABC is  [#permalink]

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

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

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

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New post 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.

Answer: A

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