Which of the following sets of numbers could not represent the three sides of a right triangle? O {24, 32, 40} O {38, 80, 89} O {48, 55, 73} 0 {10, 24, 26}
Which of the following sets of numbers could not represent the three sides of a right triangle? O {24, 32, 40} O {38, 80, 89} O {48, 55, 73} 0 {10, 24, 26}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
instructions in photo
![**Mathematics Question: Determining Right Triangles**
**Which of the following sets of numbers could **not** represent the three sides of a right triangle?**
1. ( ) {24, 32, 40}
2. ( ) {38, 80, 89}
3. ( ) {48, 55, 73}
4. ( ) {10, 24, 26}
To determine which of these sets does not form a right triangle, recall that for any set of three numbers to represent the sides of a right triangle, the Pythagorean theorem must hold true:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side of the triangle), and \( a \) and \( b \) are the other two sides.
Evaluate each set:
1. **{24, 32, 40}**
\[ 24^2 + 32^2 = 576 + 1024 = 1600 \]
\[ 40^2 = 1600 \]
This set satisfies the Pythagorean theorem.
2. **{38, 80, 89}**
\[ 38^2 + 80^2 = 1444 + 6400 = 7844 \]
\[ 89^2 = 7921 \]
This set does not satisfy the Pythagorean theorem.
3. **{48, 55, 73}**
\[ 48^2 + 55^2 = 2304 + 3025 = 5329 \]
\[ 73^2 = 5329 \]
This set satisfies the Pythagorean theorem.
4. **{10, 24, 26}**
\[ 10^2 + 24^2 = 100 + 576 = 676 \]
\[ 26^2 = 676 \]
This set satisfies the Pythagorean theorem.
The set **{38, 80, 89}** could **not** represent the three sides of a right triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddc6b782-5568-4e4b-a41c-c5410dd3aea4%2F872302fb-4f2c-42df-a167-05ca5c64a8e8%2Feh5qcdk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Question: Determining Right Triangles**
**Which of the following sets of numbers could **not** represent the three sides of a right triangle?**
1. ( ) {24, 32, 40}
2. ( ) {38, 80, 89}
3. ( ) {48, 55, 73}
4. ( ) {10, 24, 26}
To determine which of these sets does not form a right triangle, recall that for any set of three numbers to represent the sides of a right triangle, the Pythagorean theorem must hold true:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side of the triangle), and \( a \) and \( b \) are the other two sides.
Evaluate each set:
1. **{24, 32, 40}**
\[ 24^2 + 32^2 = 576 + 1024 = 1600 \]
\[ 40^2 = 1600 \]
This set satisfies the Pythagorean theorem.
2. **{38, 80, 89}**
\[ 38^2 + 80^2 = 1444 + 6400 = 7844 \]
\[ 89^2 = 7921 \]
This set does not satisfy the Pythagorean theorem.
3. **{48, 55, 73}**
\[ 48^2 + 55^2 = 2304 + 3025 = 5329 \]
\[ 73^2 = 5329 \]
This set satisfies the Pythagorean theorem.
4. **{10, 24, 26}**
\[ 10^2 + 24^2 = 100 + 576 = 676 \]
\[ 26^2 = 676 \]
This set satisfies the Pythagorean theorem.
The set **{38, 80, 89}** could **not** represent the three sides of a right triangle.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
