To determine whether the numbers 24, 32, and 40 can form a right triangle, we can apply the Pythagorean theorem. The Pythagorean theorem states that for a right triangle with sides of lengths a, b, and hypotenuse c, the following equation holds:
a² + b² = c²
In our case, we need to identify the longest number among 24, 32, and 40, as this will serve as the hypotenuse. The longest number here is 40.
Now we can assign:
- a = 24
- b = 32
- c = 40
Next, we will calculate a² and b²:
- a² = 24² = 576
- b² = 32² = 1024
Now, we sum a² and b²:
a² + b² = 576 + 1024 = 1600
Now, we will calculate c²:
- c² = 40² = 1600
Finally, we check if a² + b² = c²:
Since 1600 = 1600, the equation holds true.
Thus, we can conclude that the numbers 24, 32, and 40 can indeed form a right triangle.