VIC problem

[poonamchiK]

If there are 2 corresponding angle triangles and one has an area twice the other. then in therms of s (smaller triangle's base) what is S (bigger triangle's base)
a. √ 2s /2
b. √ 3s/2
c. √2s
d. √ 3s
e. 2s

correct answer c. ?

[gokul_nair1984]

I assume 2 corresponding angled traingles mean that 2 angles are corresponding in both triangles. Thus the third angle also has to be same. Therefore, by AAA (Angle-Angle-Angle) rule we can prove both the triangles are similar in nature.

Furthermore just by heart this rule ( It can be proven)

If two similar triangles have sides in the ratio a/b , then their areas are in the ratio (a^2)/(b^2)----(1)

Coming to the problem,
Let's assume the area of the smaller triangle is x
Therefore, the area of the larger triangle is 2x

Substituting this information in (1) we get,
(s^2)/(S^2)=x/2x

=>(s^2)/(S^2)=1/2

Therefore, S= √2s

[RonPurewal]

here's a big fat existing thread on this problem:
post19973.html