Question

a rectangular lawn is surrounded by a path of width 2 m on all sides. now if the length of the lawn is reduced by 2 m the lawn becomes a square lawn and the area of path becomes 13/11 times, what is the length of the original lawn

Answer 1

Let the length of the lawn be x then the width of the lawn is y

The outer length is x + 4 and width is y + 4

y = (x - 2)

The area of the path is :

x(x - 2) = x² - 2x

(x + 4)(x + 4 - 2) = x² + 6x + 8

x² + 6x + 8 - x² + 2x = 8x + 8

The new length when the length is reduced by 2m is:

x - 2 This equals to the width.

The outer dimensions will be :

Length = x + 6

Width = x + 4

The area of the path :

(x + 4)(x + 6) = x² + 8x + 12

(x - 2)² = x² - 4x + 4

The difference of the two gives :

12x + 8

12 x + 8 = 13/11(8x + 8)

132 x + 88 = 104x + 104

28x = 16

x = 4/7 cm

Answer 2

Answer:x = 4/7 cm

Step-by-step explanation: