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We can use the Pythagorean theorem to solve for the missing side \( x \) in this right triangle. The Pythagorean theorem is given as:

\[
a^2 + b^2 = c^2
\]

Where \( a \) and \( b \) are the legs of the right triangle, and \( c \) is the hypotenuse. In this triangle, the hypotenuse is the side labeled \( x \), and the legs are 11 cm and 16 cm.

So, we will calculate \( x \) by solving:

\[
x^2 = 11^2 + 16^2
\]

\[
x^2 = 121 + 256
\]

\[
x^2 = 377
\]

Now, take the square root of both sides to find \( x \):

\[
x = \sqrt{377} \approx 19.4 \, \text{cm}
\]

Thus, the length of the missing side \( x \) is approximately **19.4 cm**.

Would you like a further breakdown or have any questions?

Here are 5 related questions for deeper understanding:
1. How can the Pythagorean theorem be used in different types of right triangles?
2. Can the Pythagorean theorem be applied in non-right triangles? Why or why not?
3. What is the significance of the hypotenuse in a right triangle?
4. How do we estimate square roots when solving for a missing side in the Pythagorean theorem?
5. In what real-life scenarios can you apply the Pythagorean theorem?

**Tip:** Always double-check your calculations when solving square roots to avoid small errors that may affect accuracy.

Given a right triangle with legs measuring 11 cm and 16 cm, estimate the length of the missing hypotenuse side (x) to the nearest tenth of a centimeter.

Learn how to estimate the hypotenuse of a right triangle using the Pythagorean theorem. With legs measuring 11 cm and 16 cm, this step-by-step guide walks you through the solution process. Suitable for students in Grades 6-9.

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