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Answer :
To solve for the width of a rectangle given its perimeter and length, we need to use the formula for the perimeter of a rectangle:
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]
In this problem, the perimeter is 82 centimeters, and the length is 18 centimeters. We will plug these values into the formula to find the width.
1. Start with the formula for the perimeter:
[tex]\[
2 \times (\text{Length} + \text{Width}) = \text{Perimeter}
\][/tex]
2. Substitute the known values into the formula:
[tex]\[
2 \times (18 + \text{Width}) = 82
\][/tex]
3. Distribute the 2 on the left side:
[tex]\[
2 \times 18 + 2 \times \text{Width} = 82
\][/tex]
4. Calculate [tex]\(2 \times 18\)[/tex]:
[tex]\[
36 + 2 \times \text{Width} = 82
\][/tex]
5. To isolate [tex]\(2 \times \text{Width}\)[/tex], subtract 36 from both sides:
[tex]\[
2 \times \text{Width} = 82 - 36
\][/tex]
6. Perform the subtraction:
[tex]\[
2 \times \text{Width} = 46
\][/tex]
7. Divide both sides by 2 to solve for the width:
[tex]\[
\text{Width} = \frac{46}{2}
\][/tex]
8. Calculate the result:
[tex]\[
\text{Width} = 23
\][/tex]
Therefore, the width of the rectangle is 23 centimeters. The equation that represents this situation is [tex]\(2 \times 18 + 2 \times \text{Width} = 82\)[/tex].
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]
In this problem, the perimeter is 82 centimeters, and the length is 18 centimeters. We will plug these values into the formula to find the width.
1. Start with the formula for the perimeter:
[tex]\[
2 \times (\text{Length} + \text{Width}) = \text{Perimeter}
\][/tex]
2. Substitute the known values into the formula:
[tex]\[
2 \times (18 + \text{Width}) = 82
\][/tex]
3. Distribute the 2 on the left side:
[tex]\[
2 \times 18 + 2 \times \text{Width} = 82
\][/tex]
4. Calculate [tex]\(2 \times 18\)[/tex]:
[tex]\[
36 + 2 \times \text{Width} = 82
\][/tex]
5. To isolate [tex]\(2 \times \text{Width}\)[/tex], subtract 36 from both sides:
[tex]\[
2 \times \text{Width} = 82 - 36
\][/tex]
6. Perform the subtraction:
[tex]\[
2 \times \text{Width} = 46
\][/tex]
7. Divide both sides by 2 to solve for the width:
[tex]\[
\text{Width} = \frac{46}{2}
\][/tex]
8. Calculate the result:
[tex]\[
\text{Width} = 23
\][/tex]
Therefore, the width of the rectangle is 23 centimeters. The equation that represents this situation is [tex]\(2 \times 18 + 2 \times \text{Width} = 82\)[/tex].
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