Answer:
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.
