PS Geometry Triangles Ratio Area to Side GMATPrep

[myfish]

I know that the ratio of the squares of the sides of a similar triangle is equal to the Area. However, how to apply this rule in this question seems not possible for me. If any genius out there wants to try and share, I'd appreciate.

Regards

[myfish]

I just figured it out. Very easy in fact. s2/S2 = 1/2 --> S2=2s2 --> S=Root2 x Root s2= Root2 x s

[quote="myfish"]I know that the ratio of the squares of the sides of a similar triangle is equal to the Area. However, how to apply this rule in this question seems not possible for me. If any genius out there wants to try and share, I'd appreciate.

Regards[/quote]

[Anurag@Gurome]

In the given triangles, three angles are same implies that they are similar triangles.

Property of similar triangles: In two similar triangles, the ratio of their areas is the square of the ratio of their sides.

So, Area of bigger triangle: Area of smaller triangle = S² : s² = 2
So, S² = 2s²
S = [spoiler]s√2[/spoiler]

The correct answer is C.

[GMATGuruNY]

Since the two triangles have the same combination of angles, they are similar.
Plug in a type of triangle whose characteristics are familiar.
Let each triangle be a 45-45-90 triangle.

Triangle ABC:
Let s=1.
A = (1/2)(1)(1) = 1/2.

Triangle DEF:
Since triangle DEF is twice the size, A=1.
Thus:
(1/2)(S)(S) = 1.
S²= 2.
S = √2.

The correct answer must yield √2 when S=1.

Only C works:
(√2)s = (√2)(1) = √2

The correct answer is C.

[myfish]

I really like this approach. In this case, you don't have to remember any rules or formula except the area of a triangle. Thanks so much.

[quote="GMATGuruNY"]Another approach is to plug in.
Since the two triangles have the same combination of angles, they are similar.
We should plug in a type of triangle whose characteristics are familiar.
Let each triangle be a 45-45-90 triangle.

[b]∆ABC:[/b]
Let s=1.
A = (1/2)(1)(1) = 1/2.

[b]∆DEF:[/b]
Since ∆DEF is twice the size, A=1.
Thus:
(1/2)(S)(S) = 1.
S²= 2.
S = √2. This is our target.

Now we plug s=1 into the answers to which yields our target of √2.

Only answer choice [spoiler]C[/spoiler] works:
(√2)s = (√2)(1) = √2.

The correct answer is [spoiler]C[/spoiler].[/quote]