On increasing the length and breadth of a rectangle by 1 m, the area increases by 21 m2. If its length is increased by 1 m but breadth decreases by 1m, area decreases by 5 m2. the perimeter of the rectangle is:
Answer & explanation
Correct answer: option 3
Let Length of rectangle be x metre and breadth by y metre
area = xy m2
Case I
(x+1) (y+1) - xy = 21
⇒ xy + x + y + 1 - xy = 21
⇒ x + y = 20
Case II
xy - (x+1) (y-1) = 5
⇒ xy - xy + x - y = 4
⇒ x - y = 4
On solving, x = 12, y = 8
∴ perimeter = 2(12+8) = 40 m