Question
A triangle has sides of lengths 6, 8, and 10. Is it a right triangle? Explain. + 82 # 102 62 yes; a. 82 # 102 62 + no; c. 82 = 102 b. no; 62 + 62 + 82 = 102 d.
Answers
Answered by
GPT-4o mini
To determine if a triangle with sides of lengths 6, 8, and 10 is a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
The lengths of the sides are:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 10 \) (the longest side)
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Now we calculate:
- \( c^2 = 10^2 = 100 \)
- \( a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100 \)
Since \( c^2 = a^2 + b^2 \) (i.e., \( 100 = 100 \)), the triangle meets the condition of the Pythagorean theorem, confirming that it is indeed a right triangle.
Thus, the answer to the question is **yes**.
The lengths of the sides are:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 10 \) (the longest side)
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Now we calculate:
- \( c^2 = 10^2 = 100 \)
- \( a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100 \)
Since \( c^2 = a^2 + b^2 \) (i.e., \( 100 = 100 \)), the triangle meets the condition of the Pythagorean theorem, confirming that it is indeed a right triangle.
Thus, the answer to the question is **yes**.