Question

Sophia is building a rectangular garden and wants to write an equation to represent the perimeter of the garden. The length of the garden is represented by l and the width by w. The perimeter, P, of the garden is calculated by using the formula P=2l+2wIf the perimeter of the garden is 24 feet and the width is 6 feet, what is the length of the garden? Fill in the missing steps to solve the equation. NOTE: Type the numerical values into the blanks to receive credit for this question.(5 points)P=2l+2w=2l+2()24=2l+=2ll= feetSkip to navigation

Answer 1

To find the length \( l \) of the garden, we can start with the equation for the perimeter given by:

\[
P = 2l + 2w
\]

We know the perimeter \( P \) is 24 feet and the width \( w \) is 6 feet. Plugging these values into the equation gives us:

\[
24 = 2l + 2(6)
\]

Now, let's simplify the equation:

\[
24 = 2l + 12
\]

Next, we need to isolate \( 2l \). We can do this by subtracting 12 from both sides:

\[
24 - 12 = 2l
\]

This simplifies to:

\[
12 = 2l
\]

Now, to find \( l \), we divide both sides by 2:

\[
l = \frac{12}{2}
\]

This gives:

\[
l = 6 \text{ feet}
\]

So the length of the garden is **6 feet**.