The area of the smaller square
[tex]A_S=x^2[/tex]
The area of the larger square
[tex]A_L=(2x)^2=4x^2[/tex]
The area of the larger square is 42cm² more than the smaller square.
Therefore we have the equation:
[tex]A_L=A_S+42[/tex]
[tex]4x^2=x^2+42\qquad|-x^2\\\\3x^2=42\qquad|:3\\\\x^2=14\to x=\sqrt{14}\ cm[/tex]
Answer:
[tex]x=\sqrt{14}\ cm\approx3.7\ cm\\\\2x=2\sqrt{14}\ cm\approx7.5\ cm[/tex]
