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These are similar triangles. Similar triangles have sides in the same ratio.
let height of triangles be h and H
Now, for smaller triangle, side s corresponds to height h
implies, side S corresponds to height H = h/s * S
Area of small triangle = 1/2*s*h
Area of larger triangle = 1/2*S*H = 1/2 *S* (h/s *S)
Given area of larger is twice area of smaller, hence
1/2 *S* (h/s *S) = 2 * (1/2 * s*h) --- solve this
or, S = s√2
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