Q. 84.0( 40 Votes )

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 rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

Answer :

Let the length be 'x' and breadth be 'y'


Area of rectangle = length × breadth


Area of rectangle = xy


First case:


Length = x - 5


Breadth = y + 3


As, area is reduced by 8 sq. units


xy - (x - 5)(y + 3) = 8


xy - (xy + 3x - 5y - 15) = 8


xy - xy - 3x + 5y + 15 = 8


3x - 5y = 7 eq.[1]


Second case:


Length = x - 3


Breadth = y + 2


As, the area is increased by 67 units


(x - 3)(y + 2) - xy = 67


xy + 2x - 3y - 6 - xy = 67


2x - 3y = 73 eq.[2]


Multiplying eq.[1] by 2 both side, and Multiplying eq.[2] by 3 both side, we get


6x - 10y = 14 eq.[3]


6x - 9y = 219 eq.[4]


Subtracting eq.[3] from eq.[4]


6x - 9y - 6x + 10y = 219 - 14


y = 205


Using this in eq.[1]


3x - 5(205) = 7


3x - 1025 = 7


3x = 1032


x = 344


Hence, length = x = 344 units


Breadth = y = 219 units.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Goprep Genius Quiz on Linear Equations34 mins
Interactive session on Linear Equations in Two VariablesFREE Class
NCERT | Linear Equations41 mins
Quiz | Testing Your Skills on Linear Equation in Two Variables36 mins
Quiz | Important Questions on Linear Equations In Two Variables49 mins
Champ Quiz | Do you Know about Linear Equations ?35 mins
Master Linear Equations40 mins
Quiz | Imp. Qs. on Linear Equations44 mins
Quiz | Solve Problems on Linear Equations37 mins
Champ Quiz | Linear Equation45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :