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 / and the width by w. The perimeter, P, of the garden is calculated by using the formula P = 2l + 2w
If 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.

P = 2l + 2w
_ = 2l + 2 (_)
24 = 2l + _
_ = 2l
l = _ feet

Answer 1

To find the length of the garden, we can start by filling in the steps using the given information.

1. We know the formula for the perimeter is:
\[
P = 2l + 2w
\]

2. In this case, we have the perimeter \( P = 24 \) feet and the width \( w = 6 \) feet. We can substitute these values into the formula:
\[
24 = 2l + 2(6)
\]

3. Now calculate \( 2(6) \):
\[
2(6) = 12
\]

4. Substitute \( 12 \) into the equation:
\[
24 = 2l + 12
\]

5. Now, we need to isolate \( 2l \):
\[
24 - 12 = 2l
\]
\[
12 = 2l
\]

6. Now, solve for \( l \):
\[
l = \frac{12}{2}
\]
\[
l = 6 \text{ feet}
\]

So, the completed steps are:

- \( 24 = 2l + 2(6) \)
- \( 24 = 2l + 12 \)
- \( 12 = 2l \)
- \( l = 6 \) feet.