The value of x for the right triangle is equal to 16 in.
To evaluate for the unknown side length of the right triangle we use the Pythagoras rule which states that in a right-angled triangle, the square of the hypotenuse(the longest side) is equal to the sum of the squares of the other two sides.
For triangle we solve for x as follows:
using Pythagoras rule;
20² = x² + 12²
400 = x² + 144
x² = 400 - 144 {collect like terms}
x² = 256
x = √256 {take square root of both sides}
x = 16
Therefore, the unknown side lengths for the right triangle are x = 16 in.