Question

Which of the following are possible side lengths for a

right triangle?
2, 4, 6
3,4,5
6,7,9.
6, 8, 10
5, 12, 13

Answer 1

3, 4, 5

6, 8, 10

5, 12, 13

Explanation:

If you are given side lengths and must determine if it is a right angle, you will use the Pythagorean Theorem. Which states that the square length of the hypotenuse (longest side of a triangle) must equal to the sum of the square length of the two shortest.

Formula: a² + b² = c²

2, 4, 6

a² + b² = c²

(2)² + (4)² ≟ (6)²

4 + 16 ≟ 36

20 ≠ 36

3, 4, 5

a² + b² = c²

(3)² + (4)² ≟ (5)²

9 + 16 ≟ 25

25 = 25

6, 7, 9

a² + b² = c²

(6)² + (7)² ≟ (9)²

36 + 49 ≟ 81

85 ≠ 81

6, 8, 10

a² + b² = c²
(6)² + (8)² ≟ (10)²

36 + 64 ≟ 100

100 = 100

5, 12, 13

a² + b² = c²

(5)² + (12)² ≟ (13)²

25 + 144 ≟ 169

169 = 169