Directions: What could the lengths of the legs be such that the lengths of the legs are integers and *x * is an irrational number between 5 and 7?

### Hint

What is a wrong answer? How can you use this wrong answer to move towards an answer?

What does it mean to be irrational between 5 and 7?

### Answer

Here are the lengths of the legs

1 and 5,

1 and 6,

3 and 4,

3 and 5,

3 and 6,

4 and 4,

4 and 5,

2 and 5,

2 and 6

1 and 5,

1 and 6,

3 and 4,

3 and 5,

3 and 6,

4 and 4,

4 and 5,

2 and 5,

2 and 6

Source: Daniel Luevanos

What about 1 and 6 or 1 and 5

Good catch, Rachel. Those could work too!

NO ONE CARES

Should 3 and 4 be in the answer key? This would provide a rational number (5), but the question asks for an irrational number between 5 and 7.

Leg 1: 2

Leg 2: 6