### Geometry Problem: Solving for \( x \)**Problem Statement:**Find the value of \( x \) in the figure below.**Given:**- The triangle \( ABC \) is a right triangle with angle \( A \) at the right angle.- \( AD \) is perpendicular from \( A \) to \( BC \).- \( AD = 3 \)- \( DB = 9 \)- \( AB = 12 \)**Choices:**A. \( x = 3 \sqrt{3} \) B. \( x = 3 \sqrt{5} \) C. \( x = 9 \sqrt{3} \) D. \( x = 4 \)**Figure Description:**The diagram illustrates a right triangle \( ABC \) with the right angle at \( A \). The altitude \( AD \) extends from angle \( A \) to the hypotenuse \( BC \). The lengths are marked as follows:- \( AD = 3 \)- \( DB = 9 \)- \( DC \) and \( BC \) are not directly provided.To solve for \( x \), which represents the length \( AC \):1. Recognize that \( AD \) divides \( \triangle ABC \) into two smaller right triangles: \( \triangle ADB \) and \( \triangle ADC \).2. Use the property of similar triangles and the Pythagorean theorem to determine the lengths of missing segments.Your task is to solve for \( x \) using the given information and choosing from the provided options.**IV. Analysis of Options:**Critically analyze each option to determine which corresponds to the correct \( x \) given the geometric properties of the triangle.

Answered: Choose the best possible answer for…

Choose the best possible answer for each question below: Find solve for x in the figure below. A B 3 D A. x = 3√/3 C. x = 9√/3 B.x= 3√5 D. x = 4 X= 'B'C'? ABC

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 32E: There are two points on the x-axis that are located a distance of 6 units from the points 3,1....

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Question

### Geometry Problem: Solving for \( x \)

**Problem Statement:**
Find the value of \( x \) in the figure below.

**Given:**
- The triangle \( ABC \) is a right triangle with angle \( A \) at the right angle.
- \( AD \) is perpendicular from \( A \) to \( BC \).
- \( AD = 3 \)
- \( DB = 9 \)
- \( AB = 12 \)

**Choices:**
A. \( x = 3 \sqrt{3} \)
B. \( x = 3 \sqrt{5} \)
C. \( x = 9 \sqrt{3} \)
D. \( x = 4 \)

**Figure Description:**
The diagram illustrates a right triangle \( ABC \) with the right angle at \( A \). The altitude \( AD \) extends from angle \( A \) to the hypotenuse \( BC \). The lengths are marked as follows:
- \( AD = 3 \)
- \( DB = 9 \)
- \( DC \) and \( BC \) are not directly provided.

To solve for \( x \), which represents the length \( AC \):

1. Recognize that \( AD \) divides \( \triangle ABC \) into two smaller right triangles: \( \triangle ADB \) and \( \triangle ADC \).
2. Use the property of similar triangles and the Pythagorean theorem to determine the lengths of missing segments.

Your task is to solve for \( x \) using the given information and choosing from the provided options.

**IV. Analysis of Options:**
Critically analyze each option to determine which corresponds to the correct \( x \) given the geometric properties of the triangle.

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