Yes, the triangle is a right-angled triangle.

A triangle with sides in the ratio 3:4:5 is a Pythagorean triple, which satisfies the Pythagorean theorem: $a^2 + b^2 = c^2$ where $a$, $b$, and $c$ are the sides of the triangle, and $c$ is the hypotenuse.

For the ratio 3:4:5, we can check if it satisfies the Pythagorean theorem:

$3^2 + 4^2 = 5^2$ $9 + 16 = 25$ Since both sides of the equation are equal, this confirms that the triangle is a right-angled triangle.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What are other common Pythagorean triples?
2. How can the Pythagorean theorem be used to find the hypotenuse of any triangle?
3. How do you determine the area of a right-angled triangle?
4. Can you generalize the Pythagorean theorem for non-right-angled triangles?
5. How would the triangle change if the sides were doubled but maintained the same ratio?

Tip: The 3:4:5 triangle is one of the most common right-angled triangles, often used in construction for ensuring perfect right angles.