can 29 in 20 in 21 in be the sides of a right triangle

To determine if three sides can form a right triangle, we use Pythagoras' theorem, which states that for a right triangle with sides of lengths \(a\), \(b\), and \(c\), where \(c\) is the length of the hypotenuse (the longest side opposite the right angle), the following relationship holds:

\[ a^2 + b^2 = c^2 \]

For the side lengths 29 in, 20 in, and 21 in, we can check if the sides satisfy this equation with one of the sides being the hypotenuse.

Let's see if 29 in is the hypotenuse:

\[ 20^2 + 21^2 \stackrel{?}{=} 29^2 \]
\[ 400 + 441 \stackrel{?}{=} 841 \]
\[ 841 = 841 \]

So in this case, the answer is yes, the sides do form a right triangle with 29 in as the hypotenuse (the longest side), and 20 in and 21 in as the other two sides.