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Let the initial length of side = a
Area, A = a²

increase in length = 200%
200% of a =  \frac{200}{100}*a=2a
final length, a' = a + 2a = 3a
Area, A' = (3a)² = 9a²

Increase in area = 9a² - a² = 8a²
% increase =  \frac{8a^2}{a^2} × 100 = 8×100 = 800%
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Let original side be x
ten area of square=s^2=x^2
let new side be x + 200% of x= x+2x=3x
area of new square=(3x)^2=9x²
increase %=(increase/original area)*100%=(8x²/x²*100)%=800
Therefore the area of the new square will increase by a)800
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