Gmat Prep: Geometry

[chetanojha]

Please help me to understand this.

[dtweah]

Please help me to understand this.

If 3 angles of one T are equal to three angles of another T then there corresponding sides must be proportional.

Drop perpendicular height h in the smaller T and H in the bigger T.

You see that both h and H subtend the same angle x, and both s and S subtend the same angle y. Using proportionality you derive

h/H =s/S

h=sH/S

Now

Area of Big T is 2 times Area of Small T

SH/2=2(sh/2)=sh

SH/2=(s(sH/S)) using h from above
S^2 x H = 2 x s^2 x H

S= s 2^.5