# The length of a rectangular garden is 3 yd more than twice its width. The perimeter of the garden is 30 yd What are the width and length of the garden?

Nov 4, 2016

The width of the rectangular garden is 4yd and the length is 11yd.

#### Explanation:

For this problem let's call the width $w$. Then the length which is "3 yd more than twice its width" would be $\left(2 w + 3\right)$.

The formula for the perimeter of a rectangle is: $p = 2 w \cdot + 2 l$

Substituting the information provided gives:

$30 = 2 w + 2 \left(2 w + 3\right)$

Expanding what is in parenthesis, combining like terms and then solving for $w$ while keeping the equation balanced gives:

$30 = 2 w + 4 w + 6$

$30 = 6 w + 6$

$30 - 6 = 6 w + 6 - 6$

$24 = 6 w$

$\frac{24}{6} = \frac{6 w}{6}$

$w = 4$

Substituting the value of $w$ into the relationship for length gives:

$l = \left(2 \cdot 4\right) + 3$

$l = 8 + 3$

$l = 11$