Question

10. A garden is 12 m long and 8 m wide. It has a path of uniform width, all around the
garden outside it. Find the width of the path, if area of the path is the same as the area
of the garden.​

Answer 1

Step-by-step explanation:

Let the width of the path be x.

∴ length of the rectangular field and path =2x+30

and breadth =2x+24

Area of rectangular field =(30×24)

=720

Area of the rectangular field and path =(2x+30)(2x+24)

Now,

(2x+30)(2x+24)−720=360

⇒4x

2

+48x+60x+720−720=360

⇒4x

2

+108x−360=0

⇒x

2

+27x−90=0

⇒x

2

+30x−3x−90=0

⇒x(x+30)−3(x+30)=0

⇒(x+30)(x−3)=0

⇒x=−30 and x=3

Negative value is not valid,

∴ Width is 3 cm