Question

Use the Pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle. Which apply. 3,4,5. Or. 4,11,14. Or. 9,14,17. Or 8,14,16. Or. 8,15,17

Answer 1

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.