Question

The perimeter of a rectangular plot is 32 metres. If length is increased by 2 metres and breadth is decreased by one metre, the area of the plot remains unchanged. Find the dimensions of the plot.

Answer 1

Answer:

length is 67cm

Step-by-step explanation:

breadth is 98cm

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the original length be x and breadth be y.

Area of rectangle = l × b = xy

New length = x + 2

New breadth = y - 1

Area of new rectangle= (x + 2)(y - 1)

Area of new rectangle= xy - x + 2y - 2

According to Question,

Area of original rectangle = Area of new rectangle

x = 2y - 2 ...(i)

Perimeter of rectangle = 32

Perimeter of rectangle = 2(l + b)

⇒ 2(l + b)=32

⇒ 2(x + y)=32

⇒ x + y = 32/2

⇒ x + y = 16

Put the value of x from eq (i)

⇒ (2y - 2) + y = 16

⇒ 2y + y - 2 = 16

⇒ 3y = 16 +2

⇒ 3y =18

⇒ y = 18 /3

⇒ y = 6

Breadth = 6 m

Length = 10 m

Thus, the dimensions of the plot are 10 m and 6 m.