Questions: Find the length (x).

Solution Steps

The given problem involves a right triangle with sides of lengths 3, 4.5, and 5. We need to find the length of the hypotenuse, denoted as $x$.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse ($x$) is equal to the sum of the squares of the other two sides. The formula is: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the lengths of the other two sides.

Substitute the given values into the Pythagorean Theorem: $$x^2 = 4.5^2 + 3^2$$

Calculate the squares of 4.5 and 3: $$4.5^2 = 20.25$$ $$3^2 = 9$$

Add the squares of the two sides: $$x^2 = 20.25 + 9$$ $$x^2 = 29.25$$

Take the square root of both sides to solve for $x$: $$x = \sqrt{29.25}$$ $$x \approx 5.41$$

Final Answer