Answer:
Yes, the triangle with side lengths 6, 8, and 10 is a right triangle.
Explaination:
We can use the Pythagorean theorem to check if a triangle is a right triangle or not. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse). In other words:
a^2 + b^2 = c^2
where a and b are the lengths of the two shorter sides, and c is the length of the longest side (the hypotenuse).
In this case, the two shorter sides are 6 and 8, and the longest side (the hypotenuse) is 10. So we can plug these values into the equation above:
6^2 + 8^2 = 10^2
Simplifying:
36 + 64 = 100
100 = 100
Since the equation is true, this means that the triangle satisfies the Pythagorean theorem, and therefore it is a right triangle.