the area of a rectangle get reduced by 9 units when it length is reduced by 5 unit and breadth is incresed by 3 units if we increase the length by 3 unis and breadth by 2 units the area increses to 67 unit square find the dimension of the rectangle
Answers
Solution:
Let length and breadth of rectangle be x unit and y unit.
So, Area = xy
According to question,
(x - 5)(y + 3) = xy - 9
=> 3x - 5y - 6 = 0 ..........(1)
(x + 3)(y + 2) = xy + 67
=> 2x + 3y - 61 = 0 ...........(2)
We solve it by Cross multiplication method,
=> 3x - 5y - 6 = 0 ..........(1)
=> 2x + 3y - 61 = 0 ...........(2)
=> 19x = 323
=> x = 17
=> 19y = 171
=> y = 9
Hence the Length and Breadth of Rectangle is 17 and 9 units.
SOLUTION:-
We know that the area of rectangle is of the form x & y
Where,
x= length
y= breadth
A/q
(x-5)(y+3)= xy-9............(1)
(x+3)(y+2)= xy+67..........(2)
On solving the equations, we get:
Equation from (1):
xy +3x-5y-15= xy-9
=) 3x-5y= 6................(3)
Equation from (2):
=) xy+2x+3y+6= xy +67
=) 2x +3y= 61..............(4)
Now by elimination method:
On multiplying equation(3) by 2 & equation (4) by 3.
=) 6x-10y= 12...........(5)
=) 6x +9y= 183............(6)
So,
On subtracting eq. (6) from (5),we get:
=) -19y= -171
=) y= 171/19
=) y= 9
On substituting y= 9 in eq. (6), we get:
=) 6x + 9(9)= 183
=) 6x + 81 = 183
=) 6x= 183 -81
=) 6x= 102
=) x= 102/6
=) x= 17
Therefore,
The dimensions of the rectangle are:
⚫Length(x)= 17 units
⚫Breadth(y)= 9 units