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

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!

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

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 ?

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-