Question

A circular grass plot 40 m. in radius is surrounded by a ring of gravel. Find the width of the gravel so
that the area of the grass and gravel may be equal.​

Answer 1

Answer:

Area of grass plot=πr

2

=π×40

2

=1600πm

2

area of path=π×(40+x)

2

−π40

2

=π[1600+x

2

+80x−1600]

=π(x

2

+80x)

now,

1600π=2π(x

2

+80x)

x

2

+80x=800

x

2

+80x−800=0

x=−40−20

6

,−40+20

6

∴x=−40+20

6

=20

6

−40=40(

4

6

−1)

x=40(

4

6

−1)=40(

2

3

−1)

∴ width of path 40(

2

3

−1)m

Answer 2

Step-by-step explanation:

Area of grass plot=πr

2

=π×40

2

=1600πm

2

area of path=π×(40+x)

2

−π40

2

=π[1600+x

2

+80x−1600]

=π(x

2

+80x)

now,

1600π=2π(x

2

+80x)

x

2

+80x=800

x

2

+80x−800=0

x=−40−20

6

,−40+20

6

∴x=−40+20

6 =20

6

−40=40( 46 −1)

x=40( 46 −1)

=40( 23−1)

∴ width of path 40( 23 −1)m