The side length of a square ABCD is 18 inches
Each side of square ABCD is 18 inches
The midpoints of ABCD are joined to form a square MNOP
The figure is attached below
We need to find the side length of square MNOP
AMN form a Right angle triangle
We know AM =9 and AN= 9
To find MN , use Pythoagorean theorem
[tex]MN^2 = AM^2 + AN^2[/tex]
[tex]MN^2 = 9^2 + 9^2[/tex]
[tex]MN^2 = 162[/tex]
Take square root on both sides
[tex]MN= 9\sqrt{2}[/tex]
so the side of the square MNOP is [tex]9\sqrt{2}inches[/tex]
