Question

The side length of a square ABCD is 18 inches. What is the side length of the square formed by joining the midpoints of the sides of ABCD?

Answer 1

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

`MN^2 = AM^2 + AN^2`

`MN^2 = 9^2 + 9^2`

`MN^2 = 162`

Take square root on both sides

`MN= 9√(2)`

so the side of the square MNOP is
`9√(2)inches`