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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: 52278
In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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06 Jun 2017, 09:25
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00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:17) correct 41% (01:29) wrong based on 146 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 2428 times ]

_________________
Senior Manager
Joined: 24 Apr 2016
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
1
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$$\sqrt{2}$$

Intern
Joined: 15 Nov 2017
Posts: 21
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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12 Jan 2019, 14:33
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much!
quantumliner wrote:
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$$\sqrt{2}$$

Intern
Joined: 23 Apr 2016
Posts: 31
Location: Singapore
Concentration: Strategy, Technology
WE: Other (Internet and New Media)
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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13 Jan 2019, 03:20
KHow,

Ratio of all the similar sides of XYZ to xyz is Sqrt 2.
X/x = Y/y = Z/z = Sqrt 2

Let me know if you got it.

Cheers!
Shantanu Sharma
MBA and Beyond Consulting

KHow wrote:
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much!
quantumliner wrote:
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$$\sqrt{2}$$

Intern
Joined: 09 Mar 2017
Posts: 5
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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13 Jan 2019, 10:27
quantumliner wrote:
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$$\sqrt{2}$$

Why is the area of Triangle ABC/Triangle abc = X^2/x^2? Where are the squares coming from?
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z &nbs [#permalink] 13 Jan 2019, 10:27
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