Question

The perimeter of a rectangular plot of land is 36m. If the length is increased by 6m and the breadth decreased by 3 m, the area of the plot remains the same. Find the length and breadth of the plot 2

Answer 1

Answer:

length = 10 m and breadth = 8m

Step-by-step explanation:

perimeter of rectangle is equal to P = 2(l + b)

Perimeter= 2(l+ b)

Area = l× b

note that the area remains the same . keep it in mind as this will used in solution.

let l is the length and b is the breadth of rectangle

so ,

perimeter = 2(l+b)

36 = 2(l+b)

l+b=18-----equation 1

it is given that the length increased by 6 so the new length will be l+6 and breadth is decreased by 3m so new breadth will be b-3 .

now let the new length is l+6

and new breadth is b-3

Area = (l+6)(b-3)

since area remains same so equating this equation with area formula we will get:

lb= (l+6)(b-3)

lb=lb - 3l + 6b-18

lb-lb = -3l + 6b - 18

0= -3l + 6b -18

3l - 6b = -18----eqn 2

now multiplying eqn1 by 6 and adding eqn 1 and 2

6l + 6b = 108

3l - 6b = -18

9l + 0 = 90 (note that 6b and -6b cancel out each other)

9l= 90

l = 10.

put this value in eqn 1 .

l + b= 18

10+ b = 18

b= 18-10

b= 8