Question
2- The width of a rectangle is \( 2 x^{2}+9 x-7 \) and the length is \( x^{2}-9 \). Find the perimeter of the rectangle.
Ask by Sanders Harmon. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The perimeter of the rectangle is \( 6x^{2} + 18x - 32 \).
Solution
To find the perimeter of a rectangle, you can use the formula:
\[
\text{Perimeter} = 2 \times (\text{Width} + \text{Length})
\]
Given:
- **Width** = \( 2x^{2} + 9x - 7 \)
- **Length** = \( x^{2} - 9 \)
Let's calculate the perimeter step by step.
1. **Add the Width and Length:**
\[
\text{Width} + \text{Length} = (2x^{2} + 9x - 7) + (x^{2} - 9)
\]
Combine like terms:
\[
= 2x^{2} + x^{2} + 9x - 7 - 9
\]
\[
= 3x^{2} + 9x - 16
\]
2. **Multiply by 2 to find the Perimeter:**
\[
\text{Perimeter} = 2 \times (3x^{2} + 9x - 16)
\]
Distribute the 2:
\[
= 6x^{2} + 18x - 32
\]
**Final Answer:**
\[
\text{Perimeter} = 6x^{2} + 18x - 32
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the perimeter of a rectangle, you need to add together the lengths of all four sides. The perimeter \( P \) is given by the formula: \[ P = 2(\text{length} + \text{width}) \] In this case, the width is \( 2 x^{2}+9 x-7 \) and the length is \( x^{2}-9 \). First, let's find the sum of the length and width: \[ \text{length} + \text{width} = (x^{2} - 9) + (2x^{2} + 9x - 7) \] Now, combine like terms: \[ = x^{2} + 2x^{2} + 9x - 9 - 7 \] \[ = 3x^{2} + 9x - 16 \] Now, plug this back into the formula for the perimeter: \[ P = 2(3x^{2} + 9x - 16) \] Distributing the 2 gives: \[ P = 6x^{2} + 18x - 32 \] So, the perimeter of the rectangle is: \[ \boxed{6x^{2} + 18x - 32} \]
