Question

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?

Answer 1

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.