Question

If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of the rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

Answer 1

Let the length be land the breadth be b.
Area of rectangle = lb
Length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units.
(I- 5)(b+ 3)=Ib- 8
$\Rightarrow$ lb - 5b + 3I- 15 = lb - 8
$\Rightarrow$ 3I- 5b = 7 ....(I)
If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units.
(I- 5 )( b + 3)=Ib-8
$\Rightarrow$ lb - 3b + 21- 6 = lb + 67
$\Rightarrow$ 2I- 3b = 73 .....(II)
Multiply (I) with 2 and (II) with 3
6I- 10b = 14 ......(III)
6I- 9b = 219 .......(IV)
Subtracting from (III) - (IV)
b = 205
Putting this value in (I) we get
31 - 5 (205) = 7
$\Rightarrow$ 3I = 7 + 1025 = 1032
$\Rightarrow$I= 344
Thus, length = 344 units and breadth = 205 units.