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+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.



NOTE: Type the numerical values into the blanks to receive credit for this question.

(5 points)
P=2l+2w

=2l+2
(
)

24=2l+

=2l

l=
feet

Answer 1

To find the length of the garden, we can start by using the perimeter equation and substituting the known values for the perimeter (P) and the width (w).

1. Start with the equation for perimeter:
\[
P = 2l + 2w
\]

2. Substitute the known values. We know \( P = 24 \) feet and \( w = 6 \) feet:
\[
24 = 2l + 2(6)
\]

3. Now calculate \( 2(6) \):
\[
24 = 2l + 12
\]

4. Next, we isolate \( 2l \) by subtracting 12 from both sides:
\[
24 - 12 = 2l
\]
\[
12 = 2l
\]

5. Finally, divide both sides by 2 to find \( l \):
\[
l = \frac{12}{2}
\]
\[
l = 6 \text{ feet}
\]

So the missing steps filled in are:

- The equation P was \( P = 2l + 2(6) \)
- The calculation \( 2(6) \) gives \( 12 \)
- The equation becomes \( 24 = 2l + 12 \)
- Simplifying gives \( 12 = 2l \)
- Therefore, \( l = 6 \) feet.