Explanation:

- We know the area of a square and a rectangle are equal.

- Let the side of the square be "s" cm. So, its area is \(s^2\).

- Given: Length of the rectangle is \(s + 5\) cm. Breadth is \(s - 4\) cm.

- The area of the rectangle is \((s + 5) \times (s - 4)\).

- Equating both areas: \(s^2 = (s + 5)(s - 4)\).

- On expanding and simplifying: \(s^2 = s^2 + 5s - 4s - 20\).

- Which simplifies to: \(0 = s - 20\).

- So, the side of the square, \(s = 20\) cm.

- Length of rectangle = \(20 + 5 = 25\) cm. Breadth = \(20 - 4 = 16\) cm.

- Perimeter of rectangle is \(2 \times (25 + 16) = 82\) cm.

Option:2, 82 cm is correct.

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