Question 1114956
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The condition says


(x+5)^2 = 4x^2


where x is the original dimension of the house.


x^2 + 10x + 25 = 4x^2  ====>

3x^2 - 10x - 25 = 0

x = {{{(10 +- sqrt(10^2 - 4*3*(-25)))/(2*3)}}} = {{{(10 +- 20)/6}}}.


We are looking for the positive root, which is x = 5.


<U>Answer</U>.  The original size of the square house was 5 meters.  The extended size is 10 meters.
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Solved.