Question

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.​

Answer 1

Answer:

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Step-by-step explanation:

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