The problem shown in the image involves finding the missing side $x$ of a right triangle using the Pythagorean theorem. The Pythagorean theorem is:

$a^2 + b^2 = c^2$

Here, $c$ is the hypotenuse (the longest side), and $a$ and $b$ are the other two sides. From the image:

• Hypotenuse ($c$) = $40$
• One side ($a$) = $9$
• Missing side ($b$) = $x$

Using the Pythagorean theorem:

$9^2 + x^2 = 40^2$

Step-by-step solution:

1. Square the known values: $9^2 = 81, \quad 40^2 = 1600$

2. Substitute into the equation: $81 + x^2 = 1600$

3. Isolate $x^2$: $x^2 = 1600 - 81 = 1519$

4. Solve for $x$ by taking the square root: $x = \sqrt{1519}$

5. Approximate the square root: $x \approx 38.97$

Final Answer:

$x \approx 38.97$

Would you like me to clarify any steps or provide further details?

Here are 5 related questions to expand your understanding:

1. How do you determine which side is the hypotenuse in a right triangle?
2. Can the Pythagorean theorem be used for non-right triangles?
3. How do you simplify square roots when the result is not a perfect square?
4. What is the importance of checking if the triangle dimensions satisfy the triangle inequality?
5. How is the Pythagorean theorem applied in real-world contexts like construction or navigation?

Tip:

Always double-check which side is the hypotenuse before applying the Pythagorean theorem!