Question

Determine whether the given lengths can be side lengths of right triangle.

Answer 1

Answers

1. YES

2. NO

3. YES

4. NO

5. NO

6. YES

Explanation

A right triangle has a property that it side length must meet. That is the pythagorean theorem.

It states that; For a right triangle ABC, c²=a²+b². Where a, b and c are the opposite side lengths to angle A,B and C respectively.

Q1

15, 36, 39

The longer side is our c.

39² = 36² + 15²

1521 = 1296 + 225

1521 = 1521

This is true. So the side lengths are for a right triangle.

Q2

3, 7, 10

The longer side is our c.

10² = 2² + 7²

100 = 4 + 49

100 = 53

This is not true. So the side lengths are NOT for a right triangle.

Q3

The longer side is our c.

8, 15, 17

17² = 8² + 15²

289 =64 + 225

289 = 289

This is true. So the side lengths are for a right triangle.

Q4

The long side is our c.

Root3, Root4, Root5

(√5)² = (√4)² + (√3)²

5 = 4 + 3

5 = 7

This is not true. So the side lengths are NOT for a right triangle.

Q5

The longer side is our c.

6, 7, 8,

8² = 6² + 7²

64 = 36 + 49

64 = 85

This is not true. So the side lengths NOT are for a right triangle.

Q6.

The longer side is always the c

12, 16, 20

20² = 12² + 16²

400 = 144 + 256

400 = 400

This is true. So the side lengths are for a right triangle.