Question
7. The perimeter of a rectangle is 33 inches. - The rectangle has a width of 4 inches. - The rectangle has a length of 2.5 x inches. What is the value of x ? *Must show work*
Ask by Clark Greene. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 5 \)
Solution
To find the value of \( x \) in the given rectangle problem, we can follow these steps:
1. **Understand the formula for the perimeter of a rectangle**:
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (L + W)
\]
where \( L \) is the length and \( W \) is the width.
2. **Identify the known values**:
- The perimeter \( P = 33 \) inches.
- The width \( W = 4 \) inches.
- The length \( L = 2.5x \) inches.
3. **Substitute the known values into the perimeter formula**:
\[
33 = 2 \times (2.5x + 4)
\]
4. **Simplify the equation**:
First, divide both sides by 2:
\[
16.5 = 2.5x + 4
\]
5. **Isolate the term with \( x \)**:
Subtract 4 from both sides:
\[
16.5 - 4 = 2.5x
\]
\[
12.5 = 2.5x
\]
6. **Solve for \( x \)**:
Divide both sides by 2.5:
\[
x = \frac{12.5}{2.5}
\]
Now, let's calculate the value of \( x \).
\[
x = 5
\]
Thus, the value of \( x \) is \( 5 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the value of \( x \), we start with the formula for the perimeter of a rectangle, which is given by: \[ P = 2(\text{length} + \text{width}) \] Given that the perimeter \( P \) is 33 inches and the width is 4 inches, we can set up the equation as follows: \[ 33 = 2(2.5x + 4) \] Now, let's solve for \( x \): 1. Divide both sides by 2 to simplify: \[ 16.5 = 2.5x + 4 \] 2. Next, subtract 4 from both sides: \[ 16.5 - 4 = 2.5x \] \[ 12.5 = 2.5x \] 3. Now, divide by 2.5 to isolate \( x \): \[ x = \frac{12.5}{2.5} \] 4. Simplifying this gives: \[ x = 5 \] Thus, the value of \( x \) is 5. So the final answer is \( x = 5 \).
