Answer:
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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