for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, if the two legs are 20 and 21, and the hypotenuse is $x$. Then $x^{2}=20^{2}+21^{2}$.

Step2: Calculate the squares

$20^{2}=20\times20 = 400$ and $21^{2}=21\times21=441$. So $x^{2}=400 + 441$.

Step3: Find the sum

$x^{2}=841$.

Step4: Solve for $x$

Take the square root of both sides. Since $x$ represents the side - length of a triangle (a non - negative value), $x=\sqrt{841}=29$.

Answer:

29