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605-655 Level|   Geometry|      
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Bunuel
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 06 Jun 2017, 10:25
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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

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B
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 06 Jun 2017, 11:14
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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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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 12 Jan 2019, 15:33
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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
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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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 13 Jan 2019, 04:20
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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
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
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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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 13 Jan 2019, 11:27
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quantumliner
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?
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 25 Sep 2020, 09:06
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dcwanderer30
quantumliner
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?


Hi ! is there some kind of rule for X^2/x^2 for similar triangles ?
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 25 Sep 2020, 23:50
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Since we are given that the 2 Triangles are Similar, the Ratio of the Similar Triangles Area:


Area ABC / Area abc = 2 / 1


Ratio of the Corresponding Sides of the 2 Triangles will be in the Ratio that is the square root of the Area Ratio in its most simplified Form


Side ABC / Side abc = sqrt(2) / sqrt(1)


Side X on Triangle ABC Corresponds to Side x on Triangle abc. The 2 Sides will be in the Side Ratio given above.


Side ABC / Side abc = sqrt(2) / 1 = X / x


X = "in terms of x" = sqrt(2) * x

-B-
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In the figure above, triangle abc is similar to triangle ABC. X, Y, Z 24 Jan 2023, 07:57
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↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




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

Given that △ abc and △ ABC are similar and the area of △ ABC is twice the area of △ abc.

=> \(\frac{Area Of △ ABC }{ Area Of △ abc} = (\frac{X }{ x})^2\)
=> \(\frac{2 * Area Of △ abc }{ Area Of △ abc} = (\frac{X }{ x})^2\)
=> \(\frac{X }{ x}\) = \(\sqrt{2}\)
=> X = x * \(\sqrt{2}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Similar Triangles

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