# Pythagorean Inequality

Directions: Using the digits 1 through 6 at most one time each, place a digit in each box to find three side lengths that are two-digits each and form an acute triangle.

### Hint

How can you make sure that it is a triangle?
How can you use the Pythagorean Theorem to make sure it is an obtuse triangle?
How is the Pythagorean Theorem for an obtuse triangle than the Pythagorean Theorem for a right triangle?

### Answer

Number of Unique Solutions: 16
1: 23,46,51
2: 25,36,41
3: 26,35,41
4: 31,46,52
5: 31,54,62
6: 32,46,51
7: 32,54,61
8: 36,41,52
9: 36,42,51
10: 41,52,63
11: 42,51,63
12: 42,53,61
13: 43,51,62
14: 52,34,61
15: 52,43,61
16: 53,41,62

Source: Samantha Cruz

## Similar Triangles 2

Directions: Using the digits 0 to 9 at most one time each, create two similar …

### 4 comments

1. The hints reference obtuse triangles rather than acute ones, and the last one seems to be missing a word.

2. Elise Levin-Guracar

Is there a way to find the triple without guess and check?

3. I think there are multiple right answers.