Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Question:**
The perimeter of a square is 56 cm. What is the approximate length of its diagonal?
**Options:**
- [ ] 10.6 cm
- [ ] 14.0 cm
- [ ] 15.0 cm
- [ ] 19.8 cm
**Explanation of the Problem and How to Solve It:**
To find the length of the diagonal of a square with a given perimeter, follow these steps:
1. **Find the Side Length of the Square:**
- The formula for the perimeter of a square is \( P = 4s \), where \( s \) is the length of a side.
- Given that the perimeter (P) is 56 cm, you can set up the equation:
\[ 4s = 56 \]
- Solving for \( s \):
\[ s = \frac{56}{4} = 14 \text{ cm} \]
2. **Calculate the Diagonal Length:**
- The diagonal of a square can be found using the Pythagorean theorem. For a square, the diagonal \( d \) forms a right triangle with the two sides of the square.
- The formula for the diagonal \( d \) is:
\[ d = s\sqrt{2} \]
- Plugging in the side length calculated:
\[ d = 14\sqrt{2} \approx 14 \times 1.414 = 19.8 \text{ cm} \]
So, the approximate length of the diagonal is **19.8 cm**.
**Answer:**
- [ ] 10.6 cm
- [ ] 14.0 cm
- [ ] 15.0 cm
- [x] 19.8 cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Fcb2fd02b-6655-4365-b039-0784398e8dcb%2Fkq1i7h6.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The perimeter of a square is 56 cm. What is the approximate length of its diagonal?
**Options:**
- [ ] 10.6 cm
- [ ] 14.0 cm
- [ ] 15.0 cm
- [ ] 19.8 cm
**Explanation of the Problem and How to Solve It:**
To find the length of the diagonal of a square with a given perimeter, follow these steps:
1. **Find the Side Length of the Square:**
- The formula for the perimeter of a square is \( P = 4s \), where \( s \) is the length of a side.
- Given that the perimeter (P) is 56 cm, you can set up the equation:
\[ 4s = 56 \]
- Solving for \( s \):
\[ s = \frac{56}{4} = 14 \text{ cm} \]
2. **Calculate the Diagonal Length:**
- The diagonal of a square can be found using the Pythagorean theorem. For a square, the diagonal \( d \) forms a right triangle with the two sides of the square.
- The formula for the diagonal \( d \) is:
\[ d = s\sqrt{2} \]
- Plugging in the side length calculated:
\[ d = 14\sqrt{2} \approx 14 \times 1.414 = 19.8 \text{ cm} \]
So, the approximate length of the diagonal is **19.8 cm**.
**Answer:**
- [ ] 10.6 cm
- [ ] 14.0 cm
- [ ] 15.0 cm
- [x] 19.8 cm
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