# The length of a rectangular garden is 7 m greater than the width. the area is 78m^2. what are the dimensions for length and width?

Aug 7, 2016

$\text{Width"=6m " Length} = \left(6 + 7\right) = 13 m$

#### Explanation:

Let $\text{Width"=x m " Length} = \left(x + 7\right) m$

So by the area

$\left(x + 7\right) \cdot x = 78$

$\implies {x}^{2} + 7 x - 78 = 0$

$\implies {x}^{2} + 13 x - 6 x - 78 = 0$

$\implies x \left(x + 13\right) - 6 \left(x + 13\right) = 0$

$\implies \left(x + 13\right) \left(x - 6\right) = 0$

$\therefore x = 6$ negative solution meanigless.

$\text{Width"=6m " Length} = \left(6 + 7\right) = 13 m$