Sure, let's solve this step-by-step.
Assuming the perimeter ([tex]\( P \)[/tex]) of the rectangular garden is 60 feet.
We know that the length ([tex]\( l \)[/tex]) of the garden is twice the width ([tex]\( w \)[/tex]).
Given:
[tex]\[ l = 2w \][/tex]
We use the formula for the perimeter of a rectangle:
[tex]\[ P = 2l + 2w \][/tex]
Substitute the known values:
[tex]\[ 60 = 2(2w) + 2w \][/tex]
Simplify inside the parentheses:
[tex]\[ 60 = 4w + 2w \][/tex]
Combine like terms:
[tex]\[ 60 = 6w \][/tex]
Solve for [tex]\( w \)[/tex]:
[tex]\[ w = \frac{60}{6} \][/tex]
[tex]\[ w = 10 \][/tex]
Now that we have the width, we can find the length. Recall:
[tex]\[ l = 2w \][/tex]
[tex]\[ l = 2 \times 10 \][/tex]
[tex]\[ l = 20 \][/tex]
So, the length of your garden is 20 feet.
