Question

The perimeter of a rectangle is 36 inches. The equation for the perimeter of a rectangle is P=2l+2w
, where l represents the length and w represents the width. Fill in the table for the possible values for length and width.(3 points)
Length (in.) Width (in.)
16
10
6

Answer 1

To find the width corresponding to each given length, we can use the perimeter equation for a rectangle:

\[
P = 2l + 2w
\]

Given that the perimeter \(P\) is 36 inches, we can rearrange the equation to solve for width \(w\):

\[
36 = 2l + 2w
\]
\[
2w = 36 - 2l
\]
\[
w = \frac{36 - 2l}{2}
\]
\[
w = 18 - l
\]

Now we can fill in the table with the corresponding widths for the provided lengths:

1. For \(l = 16\):
\[
w = 18 - 16 = 2 \text{ inches}
\]

2. For \(l = 10\):
\[
w = 18 - 10 = 8 \text{ inches}
\]

3. For \(l = 6\):
\[
w = 18 - 6 = 12 \text{ inches}
\]

Now we can fill in the table:

| Length (in.) | Width (in.) |
|---------------|--------------|
| 16 | 2 |
| 10 | 8 |
| 6 | 12 |