A rectangle has an area of 364.5 cm?. If its length is 27 cm, find its perimeter.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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(#5) I’m so confused, someone please help
### Problem Description

A rectangle has an area of 364.5 cm². If its length is 27 cm, find its perimeter.

### Step-by-Step Solution

1. **Understand the given information:**
    - Area of the rectangle (A) = 364.5 cm²
    - Length of the rectangle (L) = 27 cm

2. **Recall the formula for the area of a rectangle:**
    \[
    \text{Area} = \text{Length} \times \text{Width}
    \]
    Therefore,
    \[
    364.5 = 27 \times \text{Width} \\
    \text{Width} = \frac{364.5}{27}
    \]

3. **Calculate the Width:**
    \[
    \text{Width} = 13.5 \text{ cm}
    \]

4. **Recall the formula for the perimeter of a rectangle:**
    \[
    \text{Perimeter} = 2 \times (\text{Length} + \text{Width})
    \]

5. **Calculate the Perimeter:**
    \[
    \text{Perimeter} = 2 \times (27 + 13.5) \\
    \text{Perimeter} = 2 \times 40.5 \\
    \text{Perimeter} = 81 \text{ cm}
    \]

### Conclusion

The perimeter of the rectangle is **81 cm**.
Transcribed Image Text:### Problem Description A rectangle has an area of 364.5 cm². If its length is 27 cm, find its perimeter. ### Step-by-Step Solution 1. **Understand the given information:** - Area of the rectangle (A) = 364.5 cm² - Length of the rectangle (L) = 27 cm 2. **Recall the formula for the area of a rectangle:** \[ \text{Area} = \text{Length} \times \text{Width} \] Therefore, \[ 364.5 = 27 \times \text{Width} \\ \text{Width} = \frac{364.5}{27} \] 3. **Calculate the Width:** \[ \text{Width} = 13.5 \text{ cm} \] 4. **Recall the formula for the perimeter of a rectangle:** \[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \] 5. **Calculate the Perimeter:** \[ \text{Perimeter} = 2 \times (27 + 13.5) \\ \text{Perimeter} = 2 \times 40.5 \\ \text{Perimeter} = 81 \text{ cm} \] ### Conclusion The perimeter of the rectangle is **81 cm**.
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