Question

12. In the adjoining figure, ABCD is a square grassy lawn of area
729 mA path of uniform width runs all around it. If the area
of the path is 295 m. find
to the length of the boundary of the square field enclosing
the lawn and the path
) the width of the path
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