if the length and breadth of a rectangle are increased by 3 metres and 2 metres respectively. the area would increase by 52 square metres. if the length and breadth are decreased by 2 metres and 3 metres respectively. the area would decreased by 43 square metres. find the length and breadth of a rectangle?
Answers
Step-by-step explanation:
let the length be x and breadth be y.
the area of rectangle=x×y =xy
after length be increased 3m then length=x+3
after breadth be increased 2m then breadth=y+2
the new area of rectangle= (x+3)(y+2)
=xy+2x+3y+6 m^2
length is decreased 2m then length=x-2
breadth is decreased 3m then breadth= y-3
the new area of rectangle=(x-2)(y-3)
=xy-3x-2y-6 m^2
A/q
=>xy+52=xy+2x+3y+6
=>xy-xy-2x-3y=6-52
=>-2x-3y=-46 -----------eqation -1
A/q
=>xy- 43=xy-3x-2y-6
=>xy-xy+3x+2y=-6+43
=>3x+2y=37-------------eqation-2
-2x-3y=-46---×3
3x+2y=37----×2
the sum of eqation 1 ×3 and eqation 2×2
-6x-9y=-138
6x+4y=74
_________
-5y=-64
y =-64/-5=64/5
the solution of y in eqation 2
6x+4y=74
6x+4×64/5=74
6x+256/5=74
6x=74-256/5
6x=114/5
x=114/5×1/6
x=19/5
then the length=19/5m
breadth=64/5m