Let length and breadth of a rectangle is x and y. Then, as per first condition,

(x-5)(y+3)=xy-9

=> xy-5y+3x-15=xy-9

=> 3x-5y=6 .....(i)

As per second condition,

(x+3)(y+2)=xy+67

=> xy+3y+2x+6=xy+67

=> 2x + 3y = 61 .....(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 5 then adding, we get

9x - 15y = 18
10x + 15y = 305
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=> 19x = 323

=> x = \( \Large \frac{323}{19} \)=17

Hence, the length of rectangle is 17 m