Question

12. In the adjoining figure, ABCD is a square grassy lawn of area
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.
(ii) the width of the path.
A
B​

Answer 1

Answer:

Given

Area of square ABCD=729m

2

So, its side =

729

=27m

Let's take the width of path =x m

Then

Side of out field =27+x+x=(27+2x)

and area of square PQRS=(27+2x)

2

m

2

Now

Area of PQRS - Area of ABCD = Area of path

⇒(27+2x)

2

m

2

−729m

2

=295m

2

⇒729+4x

2

+108x−729=295

⇒4x

2

+108x−295=0

By using the quadratic formula, we have

a=4,b=108,c=−295

⇒x=

8

−108±

(108)

2

−4×(4)×(−295)

=

8

−108±

11664+4720

=

8

−108±128

=

8

20

=2.5

Hence, Width of the path =2.5m

Now side of square field PQRS=27+2x=(27+2×2.5)m=32m

Therefore,

Length of boundary =4×side=32×4=128m

Answer 2

Answer:

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.