Question

12. In the adjoinin
72 729 m2. A path of uniform width runs all around it. If the area
of the path is 295 m², find
(i) the length of the boundary of the square field enclosing
the lawn and the path.
11​

Answer 1

Solution :-

Area of the square lawn = 729 sq m

Area of the square = Side*Side

⇒ 729 = (Side)²

⇒ Side = √729

⇒ Side = 27 m

So, the length of each side of the square lawn is 27 m

Now,

Area of the path that runs all around the square lawn = 295 sq m (Given)

Total area of the square field = Area of the path all around the square lawn + Area of the square lawn  

⇒ 729 sq m + 295 sq m

= 1024 sq m

So, the area of the square field = 1024 sq m

Length of boundary of square field enclosing the square lawn and the path =

√1024

= 32 m

So, length of the square field enclosing the lawn and the path is 32 m

Width of the path = Length of the boundary enclosing lawn and path - length of the square lawn

⇒ 32 - 27

= 5 m

So, the width of the path is 5 m

Answer.