Question

If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is reduced by 80 cm². However, if we increase the length by 10 cm and decrease the breadth by 5 cm, its area is increased by 50 cm². Find the length and breadth of the rectangle.  

Answer 1

Let the length of rectangle be x m and breadth of rectangle be y m 

Area of rectangle = xy m² 

(x − 5) (y + 2) = xy − 80 

xy − 5y + 2x − 10 = xy − 80

2x − 5y = −70     ...(i)

(x + 10) (y − 5) = xy + 50

xy − 5x + 10y − 50 = xy + 50

−5x + 10y = 100

−x + 2y = 20    ...(ii) 

2x − 5y = −70    ...(iii)

from (i) and (ii) x = 40 m, y = 30 m

length of rectangle = 40 m  

and breadth of rectangle = 30 m