Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle?
To determine if these numbers can be the lengths of the sides of a right triangle, we can use the Pythagorean theorem, which states that for any right triangle with sides of lengths a, b, and c (where c is the longest side, the hypotenuse), the following equation holds true: a² + b² = c²
Let's first sort the numbers in ascending order: 24, 32, and 40. We will consider the 40 as the hypotenuse or the longest side of the triangle (c). Now, we just need to check if the following equation holds true: 24² + 32² = 40²
24² = 576
32² = 1024
Adding the squares of 24 and 32: 576 + 1024 = 1600
Calculating the square of 40: 40² = 1600
Since 1600 = 1600, the Pythagorean theorem holds true for these numbers. Therefore, the numbers 24, 32, and 40 can be the lengths of the three sides of a right triangle.