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Answer :
To find the length of the rectangle, we need to understand a few key points about the properties of rectangles and how the perimeter works. Here's a step-by-step solution:
1. Understand the Perimeter Formula:
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated as:
[tex]\[
P = 2 \times (\text{length} + \text{width})
\][/tex]
In this problem, the perimeter is given as 44 inches.
2. Establish the Relationship between Length and Width:
We are told that the length is 8 inches more than the width.
Let's denote the width as [tex]\( w \)[/tex]. Therefore, the length is [tex]\( w + 8 \)[/tex].
3. Substitute the Relationship into the Perimeter Formula:
Use the perimeter formula with the known perimeter of 44 inches:
[tex]\[
44 = 2 \times ((w + 8) + w)
\][/tex]
4. Simplify and Solve for the Width:
[tex]\[
44 = 2 \times (2w + 8)
\][/tex]
[tex]\[
44 = 4w + 16
\][/tex]
[tex]\[
44 - 16 = 4w
\][/tex]
[tex]\[
28 = 4w
\][/tex]
[tex]\[
w = \frac{28}{4} = 7
\][/tex]
5. Find the Length:
Since the length is 8 inches more than the width, substitute the width back into the expression for length:
[tex]\[
\text{length} = w + 8 = 7 + 8 = 15
\][/tex]
Therefore, the length of the rectangle is 15 inches. The correct answer to this question is option c) 15.
1. Understand the Perimeter Formula:
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated as:
[tex]\[
P = 2 \times (\text{length} + \text{width})
\][/tex]
In this problem, the perimeter is given as 44 inches.
2. Establish the Relationship between Length and Width:
We are told that the length is 8 inches more than the width.
Let's denote the width as [tex]\( w \)[/tex]. Therefore, the length is [tex]\( w + 8 \)[/tex].
3. Substitute the Relationship into the Perimeter Formula:
Use the perimeter formula with the known perimeter of 44 inches:
[tex]\[
44 = 2 \times ((w + 8) + w)
\][/tex]
4. Simplify and Solve for the Width:
[tex]\[
44 = 2 \times (2w + 8)
\][/tex]
[tex]\[
44 = 4w + 16
\][/tex]
[tex]\[
44 - 16 = 4w
\][/tex]
[tex]\[
28 = 4w
\][/tex]
[tex]\[
w = \frac{28}{4} = 7
\][/tex]
5. Find the Length:
Since the length is 8 inches more than the width, substitute the width back into the expression for length:
[tex]\[
\text{length} = w + 8 = 7 + 8 = 15
\][/tex]
Therefore, the length of the rectangle is 15 inches. The correct answer to this question is option c) 15.
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