Questions: Introduction to the Pythagorean Theorem For the following right triangle, find the side length x.

Introduction to the Pythagorean Theorem For the following right triangle, find the side length x.
Transcript text: Introduction to the Pythagorean Theorem For the following right triangle, find the side length $x$.
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Solution

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Solution Steps

Step 1: Identify the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is: \[ c^2 = a^2 + b^2 \]

Step 2: Assign the Given Values

In the given right triangle:

  • One leg (a) is 12
  • The other leg (b) is 16
  • The hypotenuse (c) is x
Step 3: Apply the Pythagorean Theorem

Substitute the given values into the Pythagorean Theorem: \[ x^2 = 12^2 + 16^2 \]

Step 4: Calculate the Squares

Calculate the squares of 12 and 16: \[ 12^2 = 144 \] \[ 16^2 = 256 \]

Step 5: Sum the Squares

Add the squares of the two legs: \[ 144 + 256 = 400 \]

Step 6: Solve for x

Take the square root of both sides to solve for x: \[ x = \sqrt{400} \] \[ x = 20 \]

Final Answer

The length of the side \( x \) is 20.

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