Answer :
Final answer:
A triangle with sides of lengths 28, 195, and 197 satisfies the Pythagorean theorem (a² + b² = c²), which confirms it is a right triangle.
Explanation:
To determine if a triangle with sides of lengths 28, 195, and 197 is a right triangle, we can apply the Pythagorean theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the hypotenuse (the longest side) must be equal to the sum of the squares of the lengths of the other two sides.
Let us calculate:
- a² + b² = c²
- 28² + 195² = 197²
- 784 + 38025 = 38809
- 38809 = 38809
As we can see, 784 plus 38025 indeed equals 38809. Hence, the triangle with sides 28, 195, and 197 satisfies the condition of the Pythagorean theorem and therefore is a right triangle.
