Using the Pythagorean theorem, calculate the value of x.

Given a right triangle with legs of length 3 and 4, we can use the Pythagorean theorem to find the length of the hypotenuse (x).

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (x) is equal to the sum of the squares of the lengths of the other two sides.

So, x^2 = 3^2 + 4^2
x^2 = 9 + 16
x^2 = 25
x = √25
x = 5

Therefore, the value of x is 5.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The formula for the Pythagorean theorem is:

```
a^2 + b^2 = c^2
```

where

- a and b are the lengths of the other two sides of the triangle
- c is the length of the hypotenuse

In this case, we are given that the length of the hypotenuse is 10 and the length of one of the other sides is 6. We can use the Pythagorean theorem to find the length of the other side:

```
a^2 + b^2 = c^2
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 100 - 36
b^2 = 64
b = sqrt(64)
b = 8
```

Therefore, the length of the other side of the triangle is 8.