Question

The perimeter of a rectangular plot of land is 32m.If the length is increased by 2m and breadth is decreased by 1m.The area of the plot remains the same.Find the length and breadth of the plot?

Answer 1

Answer:

Step-by-step explanation:

let length be 'l' and breadth be 'y',

given perimeter of rectangle= 32m = 2( l+b)

2(l+b)=32

⇒l+b=16 ________1

by given condition

area of rectangle = (l)(b)

and, (l+2)(b-1)=(l)(b)

⇒ (l)(b)-l+2b-2=(l)(b)

⇒ (-l)+2b-2=0

⇒ (-l)+2b=2 _______2

adding equations 1 and 2 ,

[l+b]+[ (-l) +2b]=16+2

⇒3b= 18

⇒b=6 metres

put b=6 in equation 1,

l+6=16

⇒l=10 metres

∴ the length and breadth of rectangular plot are 10 metres and 6 metres respectively.