Answer:
6 inches.
Step-by-step explanation:
Let a represent side length of larger square.
We know that area of square is square of its side length, so area of the larger square will be [tex]a^2[/tex].
The area of smaller square would be [tex]4^2[/tex].
We will use proportions to solve our given problem.
[tex]\frac{\text{Area of smaller square}}{\text{Area of larger square}}=\frac{4}{9}[/tex]
[tex]\frac{4^2}{a^2}=\frac{4}{9}[/tex]
[tex]\frac{16}{a^2}=\frac{4}{9}[/tex]
Cross multiply:
[tex]4*a^2=16*9[/tex]
[tex]\frac{4*a^2}{4}=\frac{16*9}{4}[/tex]
[tex]a^2=36[/tex]
Take square root:
[tex]a=\pm\sqrt{36}[/tex]
[tex]a=\pm 6[/tex]
Since the length cannot be negative, therefore, the side length of larger square is 6 inches.
