Explanation:

- Given, the area of the rectangle is 60 m² and perimeter is 34 m. Let the length and width be L and W.

- Using the area: \( L \times W = 60 \).

- Using the perimeter: \( 2(L + W) = 34 \) or \( L + W = 17 \).

- Solving these two equations:

- \( W = 17 - L \)

- Substitute in area equation: \( L \times (17 - L) = 60 \)

- Solve: \( L^2 - 17L + 60 = 0 \).

- Solve this quadratic: Roots are \( L = 12 \) and \( W = 5 \).

- Diagonal of the rectangle: \( \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \).

- The diagonal is the side of a square. Thus, the side of the square is 13 m.

- Area of the square: \( 13^2 = 169 \) m².

- Correct Option: Option 1: 169.

-