A triangle has sides with lengths of 39 yards, 52 yards, and 65 yards. Is it a right triangle

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Yes, the triangle with sides of 39 yards, 52 yards, and 65 yards is a right triangle.

To determine this, you can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Here's the calculation:

1. **Square the lengths of the two shorter sides:**
   - $$39^2 = 1521$$
   - $$52^2 = 2704$$

2. **Add these squares together:**
   - $$1521 + 2704 = 4225$$

3. **Square the length of the longest side (hypotenuse):**
   - $$65^2 = 4225$$

Since $$39^2 + 52^2 = 65^2$$ (i.e., $$1521 + 2704 = 4225$$), the Pythagorean theorem holds true for these side lengths. Therefore, the triangle is indeed a right triangle.

**Conclusion:**  
The triangle is a right triangle because $$39^2 + 52^2 = 65^2$$.
The triangle with sides 39 yards, 52 yards, and 65 yards is a right triangle because $$39^2 + 52^2 = 65^2$$.

A triangle has sides with lengths of 39 yards, 52 yards, and 65 yards. Is it a right triangle

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