To determine if a triangle with sides measuring 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 longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
In our case, we first identify the longest side. Here, 26 is the longest side, so we will treat it as the hypotenuse. The other two sides are 10 and 24. According to the Pythagorean Theorem, we should check whether:
262 = 102 + 242
Calculating these values:
- 262 = 676
- 102 = 100
- 242 = 576
Now we add the squares of the two shorter sides:
102 + 242 = 100 + 576 = 676
Since both sides of the equation are equal (676 = 676), we confirm that this triangle is a right triangle.
In conclusion, yes, a triangle with sides 10, 24, and 26 is indeed a right triangle, as it satisfies the conditions of the Pythagorean Theorem.