Answer:
The side length is multiplied by [tex]\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The area of the original square is equal to
[tex]A=9^{2}=81\ in^{2}[/tex]
If the area is doubled
then
The area of the larger square is
[tex]A1=(2)81=162\ in^{2}[/tex]
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the larger square
y ---> the area of the original square
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=162\ in\^{2}[/tex]
[tex]y=81\ in\^{2}[/tex]
[tex]z^{2}=\frac{162}{81}[/tex]
[tex]z^{2}=2[/tex]
[tex]z=\sqrt{2}[/tex] ------> scale factor
therefore
The side length is multiplied by [tex]\sqrt{2}[/tex]
