A triangle has sides with lengths of 40 inches, 50 inches, and 29 inches. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this case, we can consider the sides of lengths 40 inches and 29 inches as a and b, and the side of length 50 inches as c (since this is the longest side and could be the hypotenuse if the triangle is a right triangle).

So, we calculate:

40² + 29² = 50² 1600 + 841 = 2500 2441 = 2500

Since 2441 is not equal to 2500, the triangle is not a right triangle according to the Pythagorean theorem.