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The perimeter of a square is 56 cm. What is the approximate length of its diagonal? 10.6 cm O 14.0 cm O 15.0 cm O 19.8 cm

The perimeter of a square is 56 cm. What is the approximate length of its diagonal? 10.6 cm O 14.0 cm O 15.0 cm O 19.8 cm

Elementary Geometry For College Students, 7e
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
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**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
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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