Assuming H,h as Height of triangle
From Given Info
Twice the area of small triangle = Area of large triangle
Area of small triangle = (1/2) (s * h)
Area of Large triangle = (1/2) (S * H)
(1/2) (s * h) (2) = (1/2) (S * H)
(s *h) = (S * H) (1/2) -------->(1)
Now since the angles are equal the similar triangles sides/Height ratio would also be the same
S= x * s ----------->(2)
H= x * h ----------->(3)
Substituting (2) and (3) in (1)
(s*h) = (x^2)(s * h) (1/2)
x = sqrt(2)
sub this in eqn (2)
S = sqrt(2) * s
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