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The diagram represents two right triangles sharing the same hypotenuse \(x\). We can solve for \(x\) using the Pythagorean theorem twice.

### Step 1: Label the two triangles
1. **Top triangle**: The sides are 4 and 4.
2. **Bottom triangle**: The sides are 10 and 4.

### Step 2: Apply the Pythagorean theorem to both triangles

#### For the top triangle:
\[
x^2 = 4^2 + 4^2
\]
\[
x^2 = 16 + 16 = 32
\]
\[
x = \sqrt{32} \approx 5.7
\]

So, the value of \(x\) is approximately **5.7** to the nearest tenth.

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. How does the Pythagorean theorem apply to different right triangles?
2. What are the properties of a diagonal in a rectangle?
3. How can you verify your solution geometrically?
4. How does scaling affect the side lengths of similar triangles?
5. What is the significance of rational vs. irrational roots in triangle solutions?

**Tip**: Always double-check that you're applying the Pythagorean theorem correctly by ensuring you identify the right triangle and the legs.

Learn how to solve for the missing side x in a diagram with two right triangles using the Pythagorean theorem. Follow a step-by-step solution applying the formula a^2 + b^2 = c^2. This problem is appropriate for students in Grades 8-10.

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