The perimeter of the rectangular garden is 36 feet
The length of the garden is 6 feet less than twice the width.
Let x represent the width of the garden:
w=x
Then we can multiply it by 2 and subtract 6 to determine the length:
l=2x-6
Lets sketch the garden:
The perimeter of a rectangle is the summ of all its sides, that is twice the width plus twice the length:
[tex]P=2w+2l[/tex]Replace the formula with the given value of P and the expressions for w and l:
[tex]36=2x+2(2x-6)[/tex]And solve for x, first is to apply the distributive propperty of multiplications to solve the term in parentheses:
[tex]\begin{gathered} 36=2x+4x-12 \\ 36=6x-12 \\ 36+12=6x \\ 48=6x \\ \frac{48}{6}=\frac{6x}{6} \\ 8=x \end{gathered}[/tex]The width of the garden is 8 feet
Now calculate the length of the garden:
[tex]\begin{gathered} l=2x-6 \\ l=2\cdot8-6 \\ l=16-6 \\ l=10 \end{gathered}[/tex]The length of the garden is 10 feet
