A rectangular garden has an area of 120 square feet. If the width of the garden is 2 less feet than the length of the garden, what are the width and length of the garden?

1 Answer
Jan 28, 2018

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

rArr x^2 - 2x = 120

rArr x^2 - 2x - 120 = 0 [Transposing 120 to the L.H.S]

rArr x^2 + 10x - 12x - 120 = 0 [Breaking -2x as 10x - 12x]

rArr x(x + 10) - 12(x + 10) = 0 [Taking the like terms aside]

rArr (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.