GMAT Prep Geometry Q

[Gmatto700]

I really need help with this one pls! I tried to do a search but couldn't find the previous post.

There are two triangles drawn - they have the same degree measure of angles x, y, and z. S1 is the base of the smaller triangle. S2 is the base of the larger triangle.

Q - In the figure, if the area of the triangle on the right (larger) is twice the area of the triangle on the left (smaller), then in terms of S1, S2 =?
a) (root2)S1/2
b) (root3)S1/2
c) (root2)S1
d) (root3)S1
e) 2S1.

Please explain.

[gogetter08]

They are similar triangles, so the bases and height of the triangle has the same ratio, say x.

ratio of areas = ratio of (1/2*base*ht)= square(x)=2(given)

So, x = root2

OA is (c)

[AleksandrM]

gogetter,

I'm not entirely clear about what you did here. Could you please expand a bit on your answer.

Thanks.

[dsk]

here is another approach ,
for similar triangles,
area(ABC)/area(XYZ) = (AB/XY)^2
by this formula,
area(larger triangle)/area(smaller) = (s2/s1)^2
since area(larger) is twice area(smaller),
2=(s2/s1)^2
hence,s2 = (root2)s1 ===> (c)

[g_beatthegmat]

Experts, is this really a probable type of question for the GMAT? Does concepts of Similar triangles get tested in the geometry portion?

Or they expect us to solve this by actually deriving the similar triangle's properties such as the ones mentioned to answer this question?

Thanks.

[Ian Stewart]

Experts, is this really a probable type of question for the GMAT? Does concepts of Similar triangles get tested in the geometry portion?

I've certainly seen the problem in the original post before, and I'm pretty sure it is a real GMAT question. In any case, similar triangles questions definitely appear on the GMAT. You don't need to know many special properties of similar triangles- you should just know what they are (triangles with the same angles), and what that means (the corresponding sides will be in the same ratio).

[Stuart@KaplanGMAT]

Here's another discussion of the same problem, with the diagrams included:

https://www.beatthegmat.com/geometry-t11 ... 0triangles

[g_beatthegmat]

thanks much Ian and Stuart!