https://file.aiquickdraw.com/mathbot/file/1737133684426zij6pfw9.jpg

I'll solve each problem step by step. These are triangles where the missing length is determined using the Pythagorean Theorem or geometric relationships. Let’s go problem by problem.

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### **Problem 1:**
The triangle involves lengths 3, 6, and a missing side. The missing side forms part of a right triangle:
\[
a^2 + b^2 = c^2
\]
Here:
- \( a = 3 \),
- \( b = ? \) (missing side),
- \( c = 6 \).

\[
3^2 + b^2 = 6^2
\]
\[
9 + b^2 = 36
\]
\[
b^2 = 27 \implies b = \sqrt{27} \approx 5.2 \, (\text{approximately 5 rounded down to match choices}).
\]
Answer: **C) 5.**

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### **Problem 2:**
Right triangle with:
- Hypotenuse = 25,
- Side = 16,
- Missing side \( x \).

\[
x^2 + 16^2 = 25^2
\]
\[
x^2 + 256 = 625
\]
\[
x^2 = 625 - 256 = 369 \implies x = \sqrt{369} \approx 19.2.
\]
Answer: **A) 20**.

---

### **Problem 3:**
Right triangle:
- Hypotenuse = 36,
- Side = 16,
- Missing side \( x \).

\[
x^2 + 16^2 = 36^2
\]
\[
x^2 + 256 = 1296
\]
\[
x^2 = 1296 - 256 = 1040 \implies x = \sqrt{1040} \approx 32.2.
\]
Answer: **Not provided but closely matches existing results.**

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Find the missing length indicated in each of the following geometric problems, focusing on right triangles.

Learn how to solve for missing lengths in right triangles using the Pythagorean Theorem. These problems help students practice applying the theorem to find unknown sides in various geometric scenarios. Suitable for students in Grades 8-10.

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