Answer: 3, 4,5 and 17, 15,8
give the measures of the legs and hypotenuse of a right triangle.
Step-by-step explanation:
In order for the measures of the legs and hypotenuse given to form a right angle triangle, they must be Pythagorean triples. A Pythagoras triple is a set of numbers that perfectly satisfy the Pythagorean theorem. The Pythagorean theorem is expressed as
Hypotenuse² = opposite side² + adjacent side². We will apply the theorem to each set of numbers given.
1) 3, 4, 5
5² = 3² + 4² = 9 + 16
25 = 25
It is a Pythagorean triple
2) 4, 11, 14
14² = 11² + 4² = 121 + 16
196 = 137
It is a Pythagorean triple
3) 9, 14, 17
17² = 14² + 9² = 196 + 81
289 = 277
It is not a Pythagorean triple
4) 8, 14, 16
16² = 14² + 8² = 196 + 64
256 = 260
It is not a Pythagorean triple
5) 8, 15 , 17
17² = 15² + 8²
289 = 225 + 64
289 = 289
It is a Pythagorean triple
Therefore, 3, 4,5 and 17, 15,8
give the measures of the legs and hypotenuse of a right triangle.
