The exercise is analyzing whether triangle $ABC$ is a right triangle by comparing the squared sums of its side lengths using the Pythagorean theorem. Let me extract the calculations and verify the result step by step.

From the image, the provided data are:

• $AB^2 = 3.64^2$, calculated as $AB^2 = 13.2496$
• $AC^2 + BC^2 = 0.27^2 + 3.65^2$, which is broken down into:
  • $0.27^2 = 0.0729$
  • $3.65^2 = 13.3225$
  • Summing gives $AC^2 + BC^2 = 13.3954$

Verification:

The task claims that $AB^2 \neq AC^2 + BC^2$, concluding that triangle $ABC$ is not a right triangle. Let's confirm:

1. $AB^2 = 13.2496$
2. $AC^2 + BC^2 = 13.3954$
3. Comparing: $AB^2 \neq AC^2 + BC^2$ since $13.2496 \neq 13.3954$.

Correction or Conclusion:

The calculations appear correct, but if there are errors in the values, corrections could be needed. Based on this, the triangle is not a right triangle.

Would you like me to explain this further or explore deeper details?
Here are 5 related questions to expand your understanding:

1. What is the Pythagorean theorem, and why is it applied here?
2. How do we determine whether a triangle is a right triangle in general cases?
3. Can rounding errors affect results in similar problems?
4. How can this concept apply in real-world situations involving geometry?
5. What is the geometric significance of squared side lengths?

Tip: Always double-check intermediate calculations to ensure consistency and avoid rounding errors in precise math problems!