# 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?

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 $\left(x - 2\right)$ feet.

So, According to the problem,

$x \left(x - 2\right) = 120$

$\Rightarrow {x}^{2} - 2 x = 120$

$\Rightarrow {x}^{2} - 2 x - 120 = 0$ [Transposing 120 to the L.H.S]

$\Rightarrow {x}^{2} + 10 x - 12 x - 120 = 0$ [Breaking $- 2 x$ as $10 x - 12 x$]

$\Rightarrow x \left(x + 10\right) - 12 \left(x + 10\right) = 0$ [Taking the like terms aside]

$\Rightarrow \left(x + 10\right) \left(x - 12\right) = 0$ [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, $x = - 10 \mathmr{and} 12$

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 $\left(12 - 2\right)$ feet = $10$ feet.