175k views
2 votes
Which set of side lengths can be the sides of a right triangle?

6, 8, 10

6, 8, 14

6, 6, 18

12, 25, 169

User Sze
by
7.7k points

1 Answer

6 votes

Answer:

(a) 6, 8, 10

Explanation:

You want to know the side lengths that form a right triangle from among the choices offered.

Triangle

First, we can eliminate all choices where the side lengths cannot form a triangle. A triangle will only be formed if the sum of the shortest two lengths exceeds the longest.

6 + 8 > 10 . . . . true, forms a triangle

6 + 8 > 14 . . . . false, not a triangle

6 + 6 > 18 . . . . false, not a triangle

12 +25 > 169 . . . . false, not a triangle

Right triangle

Already we know there is only one reasonable answer choice:

6, 8, 10

We can check to see if these lengths form a right triangle. If they do, they will satisfy the Pythagorean relation:

a² +b² = c²

6² +8² = 10²

36 + 64 = 100 . . . . true

The side lengths 6, 8, 10 can be the sides of a right triangle.

__

Additional comment

The sides 6, 8, 10, have the ratios 3:4:5. They are double the lengths of the primitive Pythagorean triple {3, 4, 5}. It can be worthwhile to remember a few such triples, as they appear often in problems involving triangles. Here are a few:

{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

The only triple that is an arithmetic sequence is 3, 4, 5. Another point worthy of note is that the sum of integer side lengths of a right triangle is always an even number.

<95141404393>

User Xleon
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories