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

Question

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

Kurtosis · Answer

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

TeamGMATIFY · Answer

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

mr7183 · Answer

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

AshokGmat2016 · Answer

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.

BrushMyQuant · Answer

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=7isO1ccQJho

Theory: If Two Triangles are Similar then ratio of their Areas is equal to square of ratio of their sides

Given that Right △ ABC and △ XYZ are similar and each side of triangle ABC is x times the corresponding side of triangle XYZ.

Let side of △ XYZ be X => Corresponding side of △ ABC = x*X = xX

=>  \frac{Area Of △ ABC }{ Area Of △ XYZ} = (\frac{xX }{ X})^2  =  x^2 
=> Area of △ XYZ =  \frac{1}{x^2}  * Area of △ ABC

So,  Answer will be A 
Hope it helps!

Watch the following video to learn the Basics of Similar Triangles

https://www.youtube.com/watch?v=n3THKzTq5ZM

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

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