length = x; breadth = y
(x + 5)(y – 3) = xy – 5
xy – 3x + 5y – 15 = xy – 5
– 3x + 5y = + 10
3x – 5y = -10 ………..(1)
(x + 3)(y + 2) = xy + 50
xy + 2x + 3y + 6 = xy + 50
2x + 3y = 44 ………..(2)
(2) × 1 ⇒ 6x -10y = -20 ……….(3)
(3) × 2 ⇒ 6x + 9y = 132 …………(4)
(3) - (4) ⇒ -19y = -152
y = \(\frac{-152}{-19}\) = 8, 2x + 3y = 44
2x + 24 = 44; 2x = 20; x = 10
∴ x = 10, y = 8
Length of the rectangle = 10 m
Breadth of the rectangle = 8m