Answer:
D. 6, 8, 10
Explanation:
You want to know which set of side lengths could form a right triangle:
- 3, 11, 20
- 5, 9, 17
- 6, 7, 8
- 6, 8, 10
Right triangle
A right triangle is a triangle with a right angle. If the side lengths don't form a triangle, then they cannot form a right triangle. They will only form a triangle if they meet the requirements of the Triangle Inequality: for sides a, b, c (shortest to longest), you must have a+b>c.
Side lengths will form a right triangle if they satisfy the Pythagorean theorem:
a² +b² = c²
3, 11, 20
3 + 11 = 14 < 20 . . . . not a triangle
5, 9, 17
5 + 9 = 14 < 17 . . . . not a triangle
6, 7, 8
6 + 7 = 13 > 8 . . . . . forms a triangle
The differences between the side lengths are 7 -6 = 1, and 8 -7 = 1. The only right triangle with side length differences of 1 is the 3-4-5 right triangle. This is not a right triangle. (It is an acute triangle.)
6, 8, 10
These side lengths have a common factor of 2. That is, the ratio of side lengths reduces to 3 : 4 : 5, noted above as forming a right triangle.
You can also demonstrate these lengths form a right triangle by showing they satisfy the Pythagorean theorem:
a² +b² = c²
6² +8² = 10²
36 +64 = 100 . . . . . true