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Length :

12

feet

Width :

10

feet

Explanation:

Let the length of the garden be

x

feet.

Therefore, the breadth or width of the garden is

(

x

−

2

)

feet.

So, According to the problem,

x

(

x

−

2

)

=

120

⇒

x

2

−

2

x

=

120

⇒

x

2

−

2

x

−

120

=

0

[Transposing 120 to the L.H.S]

⇒

x

2

+

10

x

−

12

x

−

120

=

0

[Breaking

−

2

x

as

10

x

−

12

x

]

⇒

x

(

x

+

10

)

−

12

(

x

+

10

)

=

0

[Taking the like terms aside]

⇒

(

x

+

10

)

(

x

−

12

)

=

0

[Completing the factorisation]

We know, When two real quantities are multiplied and the product is zero, then one of them or both of them should be zero.

So, Either

x

+

10

=

0

or

x

−

12

=

0

So,

x

=

−

10

or

12

As

x

indicates length,

x

can't be negative.

So,

x

=

12

.

So, The length of the garden is

12

feet and the width of the garden is

(

12

−

2

)

feet =

10

feet.

Step-by-step explanation:

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roots are from trees

step-by-step explanation: