Questions: Find the length (x).

Transcript text: Find the length $x$.

Solution

Solution Steps

Step 1: Identify the Right Triangle

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 $.

Step 2: Apply the Pythagorean Theorem

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.

Step 3: Substitute the Given Values

Substitute the given values into the Pythagorean Theorem: \[ x^2 = 4.5^2 + 3^2 \]

Step 4: Calculate the Squares

Calculate the squares of 4.5 and 3: \[ 4.5^2 = 20.25 \] \[ 3^2 = 9 \]

Step 5: Sum the Squares

Add the squares of the two sides: \[ x^2 = 20.25 + 9 \] \[ x^2 = 29.25 \]

Step 6: Solve for $ x $

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