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Explanation:

Let the length of the rectangle be x metre and breadth be y metre.

∴ xy – (x – 5) (y + 3) = 9

=> xy – (xy – 5y + 3x – 15) = 9

=> 5y – 3x + 15 = 9

=> 3x – 5y – 6 = O …..(i)

Again. (x + 3) (y + 2) – xy = 67

3y + 2x + 6 = 67

=> 2x + 3y – 61 = 0 ……….(ii)

By equation (i) × 3 + (ii) × 5

9x – 15y – 18 = 0

10x + 15y – 305 = O

19x = 323

=> x = 17 metre