Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.3: The Pythagorean Theorem
Problem 31E
Related questions
Question
![### Geometry Problem on Rectangles and Diagonals
**Problem Statement:**
ABCD is a rectangle. Find the length of the diagonal DB.
**Diagram:**
There is a rectangle labeled ABCD.
- AB and CD are the vertical sides of the rectangle, each measuring 8 feet.
- BC and AD are the horizontal sides, each measuring 6 feet.
- The diagonals AC and BD intersect at point E.
- The intersection point E is positioned at the center of the rectangle.
**Multiple Choice Options:**
- 6
- 10
- 5
- 8
In a rectangle, the diagonals are of equal length. The length of the diagonal can be found using the Pythagorean theorem:
\[ \text{Diagonal}^2 = \text{Side1}^2 + \text{Side2}^2 \]
\[ DB = \sqrt{(8)^2 + (6)^2} \]
\[ DB = \sqrt{64 + 36} \]
\[ DB = \sqrt{100} \]
\[ DB = 10 \]
The correct answer is:
- 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F037d822b-ba60-449d-bf45-a79a49d010a3%2F8d96b19f-1b7e-4f2c-881e-91348e8d063b%2Fl62cm3s_processed.png&w=3840&q=75)
Transcribed Image Text:### Geometry Problem on Rectangles and Diagonals
**Problem Statement:**
ABCD is a rectangle. Find the length of the diagonal DB.
**Diagram:**
There is a rectangle labeled ABCD.
- AB and CD are the vertical sides of the rectangle, each measuring 8 feet.
- BC and AD are the horizontal sides, each measuring 6 feet.
- The diagonals AC and BD intersect at point E.
- The intersection point E is positioned at the center of the rectangle.
**Multiple Choice Options:**
- 6
- 10
- 5
- 8
In a rectangle, the diagonals are of equal length. The length of the diagonal can be found using the Pythagorean theorem:
\[ \text{Diagonal}^2 = \text{Side1}^2 + \text{Side2}^2 \]
\[ DB = \sqrt{(8)^2 + (6)^2} \]
\[ DB = \sqrt{64 + 36} \]
\[ DB = \sqrt{100} \]
\[ DB = 10 \]
The correct answer is:
- 10
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