# You put in a flower bed measuring 20 feet by 30 feet. To finish the project you are putting in a uniform border of bark around the outside of the rectangular garden. You have enough bark to cover 336 square feet. How wide should the border be?

## I know the equation I should be using is [(20+x)(30+x)]-(20*30)=x

Apr 25, 2018

The border of bark is $4$ft wide

#### Explanation:

Length of the rectangular flower bed including border is $30 f t$

Breadth of the rectangular flower bed including border is $20 f t$

Let the border of bark be $x$ft wide.

So excluding border

length becomes $\left(30 - 2 x\right)$ ft

and breadth becomes $\left(20 - 2 x\right)$ ft

Given area of the border $336 f {t}^{2}$

So we have

$\left(20 \cdot 30\right) - \left(20 - 2 x\right) \left(30 - 2 x\right) = 336$

$\implies 20 \cdot 30 - \left(20 \cdot 30\right) + 100 x - 4 {x}^{2} = 336$

$\implies 100 x - 4 {x}^{2} = 336$

$\implies {x}^{2} - 25 x + 84 = 0$

$\implies {x}^{2} - 21 x - 4 x + 84 = 0$

$\implies x \left(x - 21\right) - 4 \left(x - 21\right) = 0$

$\implies \left(x - 21\right) \left(x - 4\right) = 0$

So $x = 4$ ft

$x = 21$ not possible