the area of rectangle gets reduced by 200 square metre if its length is reduced by 10m and with is increased by 10m if we increase the length of 5 m and breadth by 10 the area is increased by 850 m². find length and breadth of rectangle?
Answers
let the length of reactangle be "x" and breadth(or width) be "y"
according to given condition
area= l*b-200
area=xy-200
length=x-10
breadth=x+10
area of rectangle=xy-200
l*b=xy-200
(x-10)(y+10)=xy-200
x(y+10)-10(y+10)=xy-200
xy+10x-10y-100=xy-200
-xy on lhs and xy on rhs will be canceled
10x-10y= -200+100
10x-10y= -100
divide by 10
x-y= -10 -----eqn 1
according to second condition
area=xy+850
length=x+5
breadth=y+10
area of rectangle=xy+850
l*b=xy+850
(x+5)(y+10)=xy+850
xy+10x+5y+50=xy+850
-xy on LHS and xy on RHS will be canceled
10x+5y=850-50
10x+5y=800
divide by 5
2x+y=160 -----------eqn 2
now add both eqn 1 and 2
2x+y+x-y=160-10
3x=150
x=50
put x=50 in eqn 1
x-y= -10
50-y= -10
-y= -10-50
-y= -60
y=60
∴length of reactangle is 50m and breadth is 60m