Select all the following that make a right triangle:

Please check the explanation.

Step-by-step explanation:

We know that for positive integers to be Pythagorean triples, they must have to work and satisfy the Pythagorean Theorem's formula:

a² + b² = c²

Here,

a and b are the sides or legs of a right triangle

c is the hypotenuse

Let us check now:

A) 3, 4, 5

a = 3, b = 4, c = 5

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

TRUE

Thus, we conclude that (3, 4, 5) makes a right triangle.

B) 8, 15, 17

a = 8, b = 15, c = 17

a² + b² = c²

8² + 15² = 17²

64 + 225 = 289

289 = 289

TRUE

Thus, we conclude that (8, 15, 17) makes a right triangle.

C) 6, 8, 10

a = 6, b = 8, c = 10

a² + b² = c²

6² + 8² = 10²

36 + 64 = 100

100 = 100

TRUE

Thus, we conclude that (6, 8, 10) makes a right triangle.

D) 5, 12, 13

a = 5, b = 12, c = 13

a² + b² = c²

5² + 12² = 13²

25 + 144 = 169

169 = 169

TRUE

Thus, we conclude that (5, 12, 13) makes a right triangle.

E) 7, 8, 9

a = 7, b = 8, c = 9

a² + b² = c²

7² + 8² = 9²

49 + 64 = 81

113 = 81

FALSE       ∵ 113 ≠ 81

Thus, we conclude that (7, 8, 9) does not make a right triangle.

E) 7, 20, 21

a = 7, b = 20, c = 21

a² + b² = c²

7² + 20² = 21²

49 + 400 = 441

449 = 441

FALSE       ∵ 449 ≠ 441

Thus, we conclude that (7, 20, 21) does not make a right triangle.

G) 10, 11, √221

a = 10, b = 11, c = √221

a² + b² = c²

10² + 11² = (√221)²

100 + 121 = 221

221 = 221

TRUE

Thus, we conclude that (10, 11, √221) makes a right triangle.

H) 5, 8, √80

a = 5, b = 8, c = √80

a² + b² = c²

5² + 8² = (√80)²

25 + 64 = 80

89 = 80

FALSE       ∵ 89 ≠ 80

Thus, we conclude that (5, 8, √80) does not make a right triangle.

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step-by-step explanation:

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