gprep triangles

NikolayZ · Tue Nov 03, 2009 5:36 am

Ok. You have 2 similar triangles in this problem.

s is the base of small triangle, S is that of a big one.
So sides and height of a big triangle may be expressed as k*s=S and k*h=H, where s is a base, and h - is a height.
(NB: k is a coefficient, literally - a ratio of S and s)
the area of small triangle equals :
1/2*h*s
whereas the area of big one equals:
1/2*kh*ks
we know that the area of a big triangle is twice the area of a small one.
2(1/2*h*s)=1/2kh*ks
h*s=1/2kh*ks
1=1/2k^2 ==> k^2=2 and k=sqrt(2).
Hence S=s*k=sqrt(2)s.

hope it helpes.