Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle? Explain why or why not.
Yes, the numbers 24, 32, 40 can be the lengths of the three sides of a right triangle. This is because they satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, we have:
24^2 + 32^2 = 576 + 1024 = 1600
40^2 = 1600
Therefore, the numbers 24, 32, 40 satisfy the Pythagorean theorem, and can form the three sides of a right triangle.