How to Solve for A Using the Pathgreum Therum with Values 3.1mm and 1.6mm

It seems like you are referring to the Pythagorean Theorem, which is a fundamental principle in geometry used to find the length of a side in a right-angled triangle.

The Pythagorean theorem formula is:

a² + b² = c²

where:
- a and b are the legs (shorter sides),
- c is the hypotenuse (the longest side opposite the right angle).

Given values 3.1mm and 1.6mm, you can label these as a and b, and solve for A, which presumably is the hypotenuse c.

Step 1: Square the given lengths

• a² = (3.1mm)² = 9.61 mm²
• b² = (1.6mm)² = 2.56 mm²

Step 2: Add the squares

a² + b² = 9.61 + 2.56 = 12.17 mm²

Step 3: Take the square root to find A (hypotenuse)

A = √12.17 ≈ 3.49 mm

Answer: The length A is approximately 3.49 mm.

If you intended different variables or a different theorem, please clarify! But with the information provided, this is how you would solve it using the Pythagorean theorem.