length = 17 units, breadth = 9 units
Step-by-step explaination:-
Let the length and the breadth of the rectangle be x units and y units respectively.
Then the area of rectangle = xy square units
According to given conditions, we have
(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67
=> xy + 3x - 5y - 15 = xy - 9
and xy + 2x + 3x + 6 = xy + 67
=> 3x - 5y - 6 = 0......eqn(i)
and 2x + 3y - 61 = 0.....eqn(ii)
Multiplying equation (i) by 2 and equation (ii) by 3, we get...
6x - 10y - 12 = 0....eqn(iii) and,
6x + 9y - 183 = 0....eqn(iv)
Subtracting equation (iii) from equation (iv), we get...
19y - 171 = 0 => y = 9.
Substituting this value of y in equation (ii), we get
2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.
Hence, the length of rectangle = 17 units and
breadth = 9 units.
<h3>Hope it helps you!!</h3>
