The sides of a triangle are in the ratio 3 : 4 : 5 . State whether the triangle is right 
angled or not.

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.

The sides of a triangle are in the ratio 3 : 4 : 5. State whether the triangle is right-angled or not.

Discover whether a triangle with sides in the ratio 3:4:5 is right-angled using the Pythagorean theorem. This problem explains the concept of Pythagorean triples and checks the triangle's validity through the formula a^2 + b^2 = c^2. Perfect for middle school students in Grades 6-8.

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