To determine the length of the screen, we can use the Pythagorean theorem, since the screen forms a right triangle with the height, length, and diagonal.

The Pythagorean theorem states: $a^2 + b^2 = c^2$ where:

• $a$ is the height,
• $b$ is the length (what we are solving for),
• $c$ is the diagonal.

Given:

• $a = 10 \, \text{in}$,
• $c = 26 \, \text{in}$.

Substitute into the formula: $10^2 + b^2 = 26^2$ $100 + b^2 = 676$ $b^2 = 676 - 100$ $b^2 = 576$ $b = \sqrt{576} = 24 \, \text{in}.$

Final Answer:

The length of the screen is 24 inches.

Would you like further clarification or visualizations?

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Here are 5 related questions to deepen your understanding:

1. How would the dimensions change if the height were increased to 12 inches but the diagonal remained 26 inches?
2. What is the aspect ratio of this screen, and how does it relate to common screen types?
3. If the diagonal were given in centimeters instead of inches, how would the calculation differ?
4. Can the screen's area be calculated from the given dimensions? If so, how?
5. How does the Pythagorean theorem apply to other real-world objects, such as ladders against walls?

Tip: Always verify units (e.g., inches vs. centimeters) when performing calculations involving real-world objects.