State whether a triangle with the given side lengths is a right. 2,5,6

To determine whether a triangle with sides 2, 5, and 6 is a right triangle, we can use the Pythagorean Theorem, which states that for a right triangle:

\[
a^2 + b^2 = c^2
\]

Where \( a \) and \( b \) are the two smaller sides, and \( c \) is the largest side (the hypotenuse). For the given side lengths of 2, 5, and 6, the largest side is 6, so we will check if:

\[
2^2 + 5^2 = 6^2
\]

Calculating both sides:

\[
2^2 = 4, \quad 5^2 = 25, \quad 6^2 = 36
\]

\[
4 + 25 = 29 \quad \text{and} \quad 36
\]

Since 29 ≠ 36, the triangle with side lengths 2, 5, and 6 is **not** a right triangle.

Would you like further details or have any questions? Here are some related questions:

1. What are the conditions for a triangle to exist based on side lengths?
2. How do you determine the type of triangle given its sides?
3. Can we determine the angles of a triangle with these side lengths?
4. What is the Pythagorean Theorem and how does it apply to right triangles?
5. How does the Law of Cosines help in classifying triangles?

**Tip**: The sum of the squares of the two smaller sides must exactly equal the square of the largest side for a triangle to be a right triangle.

State whether a triangle with the given side lengths is a right triangle: 2, 5, 6.

Determine if a triangle with side lengths 2, 5, and 6 is a right triangle using the Pythagorean Theorem. The solution includes step-by-step calculations and a clear explanation. Perfect for students in Grades 8-10 learning about right triangles and geometric principles.

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