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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: 55670
In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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06 Jun 2017, 10:25
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61% (01:36) correct 39% (02:04) wrong based on 161 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 2996 times ]

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Joined: 24 Apr 2016
Posts: 328
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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06 Jun 2017, 11:14
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$$\sqrt{2}$$

Answer is B
Manager
Joined: 15 Nov 2017
Posts: 54
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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12 Jan 2019, 15:33
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$$\sqrt{2}$$

Answer is B
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Joined: 23 Apr 2016
Posts: 59
Location: Singapore
Concentration: Entrepreneurship, 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, 04:20
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
INSEAD Class of December 2017
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$$\sqrt{2}$$

Answer is B
Intern
Joined: 09 Mar 2017
Posts: 14
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z  [#permalink]

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13 Jan 2019, 11:27
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$$\sqrt{2}$$

Answer is B

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   [#permalink] 13 Jan 2019, 11:27
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z

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