The area of a rectangular garden is 38 1/4 square meters . the width of the garden is 4 1/2 meters .find the length of the garden.

Length : 12 feet

Width : 10 feet

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

⇒x2−2x=120

⇒x2−2x−120=0[Transposing 120 to the L.H.S]

⇒x2+10x−12x−120=0[Breaking −2x as 10x−12x]

⇒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=−10or12

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 = 10feet.