Question

What is the equation to find the dimensions of a rectangular garden with a perimeter of 54 feet and a length that is 3 feet shorter than twice its width?

Answer 1

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:

1. \( l = 2w - 3 \)
2. \( l + w = 27 \)

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