Question

A square has side length of 9 in. If the area is doubled, what happens to the side length?

Answer 1

Answer:

The side length is multiplied by $\sqrt{2}$

Step-by-step explanation:

we know that

The area of the original square is equal to

$A=9^{2}=81\ in^{2}$

If the area is doubled

then

The area of the larger square is

$A1=(2)81=162\ in^{2}$

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

$z^{2}=\frac{x}{y}$

we have

$x=162\ in\^{2}$

$y=81\ in\^{2}$

$z^{2}=\frac{162}{81}$

$z^{2}=2$

$z=\sqrt{2}$ ------> scale factor

therefore

The side length is multiplied by $\sqrt{2}$