To determine if a triangle with sides of lengths 10, 24, and 26 is a right triangle, we can use the Pythagorean theorem. This theorem 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 lengths of the other two sides.
First, we identify the longest side, which is 26. The Pythagorean theorem can be expressed as:
c² = a² + b²
Where:
- c is the length of the hypotenuse (26 in this case),
- a and b are the lengths of the other two sides (10 and 24).
Now, we will calculate:
- c² = 26² = 676
- a² + b² = 10² + 24² = 100 + 576 = 676
Since both sides of the equation are equal (676 = 676), we confirm that the triangle indeed satisfies the Pythagorean theorem.
Therefore, we can conclude that the triangle with sides of lengths 10, 24, and 26 is a right triangle.