Question

if in a rectangle the length is increased and breadth is decreased by two units each, the area is reduced by 28 square units if the length is reduced by 1 unit and breadth is increased by 2 units find the dimensions of the rectangle.

Answer 1

let the dimension be x & y respectively
By the first given condition
(x+2)(y-2)=xy-28
xy-2x+2y-4=xy-28
-2x+2y-4=-28
(multiplying both sides by -1)
2x-2y+4=28
2x-2y=24
x-y=12(divide by 2).................(1)
By the second given condition
(x-1)(y+2)=xy-1
xy+2x-y-2=xy-1
2x-y-2=-1
2x-y=1..........................................(2)
subtracting eqn (2) from (1)
x=-11
substitute x=-11 in eq n(1) x-y=12
-11-y=12
-y=12+11
-y=23
y=-23
SOLUTION:x=-11 ;y=-23
HOPE THIS HELPS

Answer 2

Answer:

let original length=x

and original breadth=y

so, original area of rectangle=length* breadth=xy

According to question

(x+2)(y-2)=xy-28

x-y= 12 - equation (1)

and

(x-1)(y+2) =xy+33

2x-y=35 - equation (2)

subtract equation (1) from (2) :-

2x-y=35

-x+y=12

x=23

put x=23 in equation (1)

23-y=12

y=11

now, length=23m

breadth=11m

Area of rectangle=23*11=253m square.