Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle? Explain why or why not.

1 answer

No, these numbers cannot be the lengths of the three sides of a right triangle.

For a triangle to be a right triangle, the length of the sides must satisfy the Pythagorean theorem: a² + b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the longest side (the hypotenuse).

Assuming that 24 and 32 are the lengths of the two shorter sides, and 40 is the length of the hypotenuse, we must check if 24² + 32² = 40².

24² = 576
32² = 1024

576 + 1024 = 1600

40² = 1600

Since 24² + 32² = 40², we can conclude that this triangle is indeed a right triangle.