The image shows a right triangle with two known sides: 40 and 9, and the unknown side labeled $x$, which we need to find.

We can use the Pythagorean Theorem to solve for $x$, which is typically used for right triangles. The Pythagorean theorem states:

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

Where:

• $a$ and $b$ are the legs of the triangle,
• $c$ is the hypotenuse (the longest side, opposite the right angle).

From the image:

• One leg $= 9$,
• The other leg $= x$,
• The hypotenuse $= 40$.

Substitute into the Pythagorean theorem:

$x^2 + 9^2 = 40^2$ $x^2 + 81 = 1600$ $x^2 = 1600 - 81$ $x^2 = 1519$

Now, take the square root of both sides to solve for $x$:

$x = \sqrt{1519} \approx 38.98$

So, the side length $x$ is approximately 38.98 units.

Would you like further clarification on any part of the solution? Here are five related questions you might find helpful:

1. What conditions are necessary to apply the Pythagorean Theorem?
2. Can the Pythagorean Theorem be used in non-right triangles?
3. How can you check if a triangle is a right triangle given its sides?
4. What other methods are there to find missing sides of triangles besides the Pythagorean Theorem?
5. How can you find the angles in a right triangle if you know all the sides?

Tip: When applying the Pythagorean theorem, always make sure the hypotenuse is correctly identified as the longest side.