Final answer:
To find the value of x in the right triangle, we use the Pythagorean theorem and solve the equation. The value of x, rounded to the nearest tenth, is 5.
Step-by-step explanation:
In a right triangle, the side opposite the right angle, which is called the hypotenuse, is always the longest side. Since the question asks for the value of x, which is the length of the hypotenuse, we need to find the length of the hypotenuse using the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle with sides of lengths a, b, and c (where c is the hypotenuse), the sum of the squares of the two shorter sides is equal to the square of the hypotenuse:
a^2 + b^2 = c^2
In this case, the given lengths of the two shorter sides are 3 and 4. To find the length of the hypotenuse (x), we can substitute these values into the equation:
3^2 + 4^2 = x^2
9 + 16 = x^2
25 = x^2
To solve for x, we take the square root of both sides:
x = √25
x = 5
So, the value of x, rounded to the nearest tenth, is 5.