To find the dimensions of the rectangular garden, we can set up equations based on the information provided.
Let the width of the garden be \( w \) feet. According to the problem, the length \( l \) is 3 feet shorter than twice the width. This relationship can be expressed as:
\[ l = 2w - 3 \]
We are also given that the perimeter \( P \) of the rectangle is 54 feet. The formula for the perimeter of a rectangle is given by:
\[ P = 2l + 2w \]
Substituting the given perimeter into the equation, we have:
\[ 2l + 2w = 54 \]
We can simplify this equation by dividing all terms by 2:
\[ l + w = 27 \]
Now we have a system of two equations:
- \( l = 2w - 3 \)
- \( l + w = 27 \)
Next, we can substitute the expression for \( l \) from the first equation into the second equation:
\[ (2w - 3) + w = 27 \]
Combining like terms gives:
\[ 3w - 3 = 27 \]
Now add 3 to both sides:
\[ 3w = 30 \]
Dividing both sides by 3 yields:
\[ w = 10 \]
Now that we have the width, we can find the length using the first equation:
\[ l = 2w - 3 = 2(10) - 3 = 20 - 3 = 17 \]
Thus, the dimensions of the rectangular garden are:
- Width \( w = 10 \) feet
- Length \( l = 17 \) feet
In conclusion, the dimensions of the garden are:
- Width: 10 feet
- Length: 17 feet