Question
A triangle has side lengths of 4.8, 28.6, 29. Is this a right triangle?
No
Yes
Not enough information
No
Yes
Not enough information
Answers
GPT-4o mini
To determine if the triangle with side lengths 4.8, 28.6, and 29 is a right triangle, we can use the Pythagorean theorem. According to this theorem, a triangle is a right triangle if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
1. Identify the longest side:
- The side lengths are 4.8, 28.6, and 29. The longest side is 29.
2. Check the Pythagorean theorem:
- According to the theorem, we need to check if:
\[
29^2 = 4.8^2 + 28.6^2
\]
Calculate each term:
- \( 29^2 = 841 \)
- \( 4.8^2 = 23.04 \)
- \( 28.6^2 = 817.96 \)
Now sum the squares of the two shorter sides:
\[
23.04 + 817.96 = 841
\]
Since \( 29^2 = 4.8^2 + 28.6^2 \) (both equal to 841), we conclude that:
Yes, this triangle is a right triangle.
1. Identify the longest side:
- The side lengths are 4.8, 28.6, and 29. The longest side is 29.
2. Check the Pythagorean theorem:
- According to the theorem, we need to check if:
\[
29^2 = 4.8^2 + 28.6^2
\]
Calculate each term:
- \( 29^2 = 841 \)
- \( 4.8^2 = 23.04 \)
- \( 28.6^2 = 817.96 \)
Now sum the squares of the two shorter sides:
\[
23.04 + 817.96 = 841
\]
Since \( 29^2 = 4.8^2 + 28.6^2 \) (both equal to 841), we conclude that:
Yes, this triangle is a right triangle.