Step-by-step explanation:
The area of the large square is the side measurement squared.
10.392 in. * 10.392 in. = 107.845184 in^2
The area of the inside square is the area of the large square minus the area of the darken area.
107.845184 in^2 - 59 in^2 = 48.845184 in^2
so, the side of the inside square is the square root of 48.845184
√48.845184 in^2 ≈ 6.958 in.
Therefore, the side of the inside square measures approximately 6.958 inches.