6.
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and
breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units,
the area increased by 61 square units. Find the dimensions of the rectangle.
Answers
Let length of rectangle = l units
And width of rectangle = b units
Area of rectangle = length * width = l*b
Now ATQ
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.
So
(l - 5)(b + 3) = lb - 9
lb + 3l – 5b – 15 = lb – 9
Subtract lb both side we get
3l - 5b = 6 …(1)
If we increase the length by 3units and the breadth by 2 units, the area increases by 67 square units.
So
(l +3)(b + 2) = lb + 67
lb + 2l + 3b + 6 = lb + 67
Subtract lb both side we get
2l + 3b = 61 …(2)
3l - 5b = 6 …(1)
Cross multiply the coefficient of l we get
6l + 9 b = 183
6l -10b =12
Subtract now we get
19 b = 171
B= 171/19 = 9
putting value of b in eqn (1)
2l + 3* 9 = 61
2l = 61 – 27
2l = 34
l = 34/2 = 17
So length of rectangle is 17 units and width is 9 units.
