There are 2 triangles with their corresponding angles equal. The base of the smaller triangle is s while that of the bigger triangle is S. If the area of the bigger triangle is twice that of the smaller one then express S in terms of s.
a) {(2^1/2)/2}s
b) {(3^1/2)/2}s
c) (2^1/2)s
d) 2s

OA: C

I got this question right in the test but am not satisfied with an assumption that I had to make. The way I solved it - I assumed that the triangles are similar; I mention it to be an assumption because AFAIK, 2 triangles are similar if their corresponding angles are equal AND their corresponding sides are proportional. In the question, the angles are mentioned to be equal but there is no mention of the sides being proportional. There was a diagram provided but it was mentioned that it is not drawn to scale, hence can't judge the proportional relationship based on the diagramatic assertion.
Now, if I consider my assumption to be true then there is a property of similar triangles that states - Ratio of areas of 2 similar triangles is equal to the ratio of the square of any 2 corresponding sides.
Hence s/S = a/A
or s/S = a/2a

Therefore, S = (2^1/2)s

Can anyone please help me get rid of this confusion with my "assumption"?


Thanks
Anirban[/img]