Question

4. The perimeter of a rectangular plot is 32 m. If the length 1 is increased by 2 m and
the breadth b is decreased by 1 m, the area of the plot remains the same. Then the values
of land b are respectively​

Answer 1

Answer:

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Step-by-step explanation:

Let the original length be x and breadth be y.

Area of original rectangle = l × b = xy

New length = x+2New breadth = y-1

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

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

area of original rectangle=area of new rectangle

xy=  xy-x+2y-2

xy-xy +x 2y-2

x=2y-2 ……………(1)

Perimeter of rectangle = 32 (Given)

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 1

(2y-2)+y=16

2y +y -2= 16

3y = 16 +2

3y=18

y= 18 /3

y=6

Breadth = 6 m

x+y= 16

x+ 6 = 16x= 16-6x= 10 Length = 10m

Hence, Length = 10 m , breadth = 6m

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